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Concept in mathematics
mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for
Unitary_representation
Map from algebra to geometric transforms
finite-dimensional projective unitary representation of G {\displaystyle G} arises from an ordinary unitary representation of G ~ {\displaystyle {\tilde
Projective_representation
Branch of mathematics that studies abstract algebraic structures
A unitary representation of a group G is a linear representation φ of G on a real or (usually) complex Hilbert space V such that φ(g) is a unitary operator
Representation_theory
Group representation
group of unitary operators. If G is a compact Lie group, every finite-dimensional representation is equivalent to a unitary one. Each representation of a
Representation_of_a_Lie_group
Physics-mathematics connection
{\displaystyle U(g)} is a projective unitary representation of G {\displaystyle G} , or possibly a mixture of unitary and anti-unitary, if G {\displaystyle G} is
Particle physics and representation theory
Particle_physics_and_representation_theory
Basic result in harmonic analysis on compact topological groups
the complete reducibility of unitary representations of G. The third part then asserts that the regular representation of G on L2(G) decomposes as the
Peter–Weyl_theorem
Semigroup action
the grading and L[a]*=-(-1)LaL*[a*]) and H is the unitary rep and also, H is a unitary representation of A. These three reps are all compatible if for
Representation of a Lie superalgebra
Representation_of_a_Lie_superalgebra
Topics referred to by the same term
Hilbert space; see self-adjoint operator Unitary equivalence of a unitary representation This disambiguation page lists mathematics articles associated with
Unitary_equivalence
Topics referred to by the same term
morphism Unitary operator Unitary transformation Unitary representation Unitarity (physics) E-unitary inverse semigroup Unitary authority Unitary state Unital
Unitary
3D combination puzzle
it to another subgroup. The Rubik's group can be endowed with a unitary representation: such a description allows the Rubik's Cube to be mapped into a
Rubik's_Cube
Mathematics term
topological group G has property (T) if the trivial representation is an isolated point in its unitary dual equipped with the Fell topology. Informally,
Kazhdan's_property_(T)
Representation of the symmetry group of spacetime in special relativity
special attention in representation theory due to its exceptional importance in physics (see History of infinite-dimensional unitary representations below)
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
spectrum. In more detail, the unitary dual is the space of all representations relevant to decomposing the regular representation. The discrete series consists
Principal series representation
Principal_series_representation
Theorem relating unitary operators to one-parameter Lie groups
continuous one-parameter unitary groups and *-representations of C 0 ( R ) . {\displaystyle C_{0}(\mathbb {R} ).} As every *-representation of C 0 ( R ) {\displaystyle
Stone's theorem on one-parameter unitary groups
Stone's_theorem_on_one-parameter_unitary_groups
Time reversal symmetry in physics
represented, in quantum mechanics either by a unitary operator, S = U, or an antiunitary one , S = UK where U is unitary, and K denotes a basis-dependent complex
T-symmetry
Representation theory of the symplectic group
In mathematics, the oscillator representation is a projective unitary representation of the symplectic group, first investigated by Irving Segal, David
Oscillator_representation
Group in group theory and physics
a unique irreducible unitary representation of H in which its centre acts by a given nontrivial character. This representation has several important
Heisenberg_group
unitary representation U of Gx on H (Here U(H) has the strong operator topology). However, it is known that a Borel measurable unitary representation
System_of_imprimitivity
Unitary representations of a Lie group
construction produces only one unitary representation of SL(2, R), the trivial representation. The finite-dimensional representation theory of the noncompact
Representation theory of SL2(R)
Representation_theory_of_SL2(R)
Type of group and algebra representation
{\displaystyle \{\rho (a):a\in A\}} . Every finite-dimensional unitary representation on a Hilbert space V {\displaystyle V} is the direct sum of irreducible
Irreducible_representation
Mathematic theorem about Riemann surfaces
is stable if and only if it comes from an irreducible projective unitary representation of the fundamental group. The main case to understand is that of
Narasimhan–Seshadri_theorem
Mathematical theorem
value of ħ), every strongly continuous unitary representation is unitarily equivalent to the standard representation with position and momentum. Let G be
Stone–von_Neumann_theorem
aspects of representation theory. See also: Glossary of representation theory Linear representation Unitary representation Trivial representation Irreducible
List of representation theory topics
List_of_representation_theory_topics
Representation theory of the symmetries of non-relativistic quantum space
invariant and central charge. Using Schur's lemma, in an irreducible unitary representation, all these Casimir invariants are multiples of the identity. Call
Representation theory of the Galilean group
Representation_theory_of_the_Galilean_group
Process of extending a representation of a subgroup to the parent group
common analytic construction of the induced representation. Let (π, V) be a continuous unitary representation of H into a Hilbert space V. We can then let:
Induced_representation
Classification of irreducible representations of the Poincaré group
Bargmann's theorem, every projective unitary representation of the Poincaré group comes from an ordinary unitary representation of its universal cover, which
Wigner's_classification
Group of unitary complex matrices with determinant of 1
special unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group
Special_unitary_group
in the unitary representation induced from σ. Branching rules for the classical groups were determined by Weyl (1946) between successive unitary groups;
Restricted_representation
Let G be a topological group and let U be a strongly continuous unitary representation of G in a separable Hilbert space H. Denote by g the family of all
Gårding_domain
Representations of finite groups, particularly on vector spaces
L_{s}} is a unitary representation of G . {\displaystyle G.} It is called left-regular representation. The right-regular representation is defined similarly
Representation theory of finite groups
Representation_theory_of_finite_groups
Representation of a group or algebra that is a direct sum of simple representations
finite-dimensional unitary representation (i.e., a representation factoring through a unitary group) is a basic example of a semisimple representation. Such a representation
Semisimple_representation
Group representation
the dual of the dual of any representation is isomorphic to the original representation. Consider a unitary representation ρ {\displaystyle \rho } of a
Dual_representation
Representation of a group or algebra in terms of an algebra with quaternionic structure
can be defined in a similar way. If V is a unitary representation and the quaternionic structure j is a unitary operator, then V admits an invariant complex
Quaternionic_representation
Type of vector space in math
quantum mechanical system. In representation theory, the Peter–Weyl theorem guarantees that any unitary representation of a compact group on a Hilbert
Hilbert_space
Quotient of special unitary group by its center
In mathematics, the projective unitary group PU(n) is the quotient of the unitary group U(n) by the right multiplication of its center, U(1), embedded
Projective_unitary_group
Representation theory of an important group in physics
is preserved. It is not, however, positive definite, so the representation is not unitary. Greiner, W.; Müller, B. (1994). Quantum Mechanics: Symmetries
Representation theory of the Poincaré group
Representation_theory_of_the_Poincaré_group
is called a cuspidal function. A cuspidal function generates a unitary representation of the group G ( A ) {\displaystyle G(\mathbb {A} )} on the complex
Cuspidal_representation
all X in g For a finite-dimensional unitary representation, the dual representation and the conjugate representation coincide. This also holds for pseudounitary
Complex conjugate representation
Complex_conjugate_representation
Bounded operators with sub-unit norm
induces an inner product and group representation φ(g) = 〈Ug v, v〉 where Ug is a (strongly continuous) unitary representation (see Bochner's theorem). Replacing
Contraction_(operator_theory)
a unitary representation of G {\displaystyle G} in a natural way. Let Φ : G → L ( H ) {\displaystyle \Phi :G\to L(H)} be a unitary representation of
Positive-definite function on a group
Positive-definite_function_on_a_group
Type of representation of a linear semisimple Lie group
different definition. More precisely, an irreducible representation is called tempered if it is unitary when restricted to the center Z, and the absolute
Tempered_representation
Mathematical theorem
introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group G on the space L2(Γ\G) of square-integrable functions
Selberg_trace_formula
action.) admissible A representation of a real reductive group is called admissible if (1) a maximal compact subgroup K acts as unitary operators and (2)
Glossary of representation theory
Glossary_of_representation_theory
Group that is a topological space with continuous group operations
Haar measure. Every unitary representation of a locally compact group can be described as a direct integral of irreducible unitary representations. (The
Topological_group
Type of group representation for locally compact groups
In mathematics, a discrete series representation is an irreducible unitary representation of a locally compact topological group G that is a subrepresentation
Discrete series representation
Discrete_series_representation
Topological algebra associated to continuous groups
the unitary representation theory of G as shown in the following Theorem. Let G be a locally compact group. If U is a strongly continuous unitary representation
Group algebra of a locally compact group
Group_algebra_of_a_locally_compact_group
Algebraic construct of interest in theoretical physics
κ(α*) = α. Note that u is a representation, but not a unitary representation. u is equivalent to the unitary representation v = ( α μ γ − 1 μ γ ∗ α ∗ )
Quantum_group
Type of measurement in quantum mechanics
{\displaystyle G} with a d 2 {\displaystyle d^{2}} -dimensional unitary representation such that ∀ | ψ ⟩ ⟨ ψ | ∈ P , ∀ U g ∈ G , U g | ψ ⟩ ∈ P {\displaystyle
SIC-POVM
Class of representations
continuous representation (π, V) of G on a complex Hilbert space V is called admissible if π restricted to K is unitary and each irreducible unitary representation
Admissible_representation
Property of measure-preserving dynamical systems
U({\mathcal {H}})} be a unitary representation on a Hilbert space H {\displaystyle {\mathcal {H}}} . In this context, the representation is sometimes called
Ergodicity
bounded representation of the integers or the real numbers is unitarizable, i.e. conjugate by an invertible operator to a unitary representation. For the
Uniformly bounded representation
Uniformly_bounded_representation
to be made to the action on functions, for L2(G/H) to afford a unitary representation of G on square-integrable functions. With appropriate scaling factors
Quasiregular_representation
Generalization of the discrete Fourier transform
equivalence relation, and each equivalence class contains a unitary representation. The unitary representations can be obtained via Weyl's unitarian trick
Fourier transform on finite groups
Fourier_transform_on_finite_groups
Duality between a group and its representations
^ , {\displaystyle {\hat {G}},} which consists of its one-dimensional unitary representations. If we allow the group G to be noncommutative, the most
Tannaka–Krein_duality
group theory, an isotypical, primary or factor representation of a group G is a unitary representation π : G ⟶ B ( H ) {\displaystyle \pi :G\longrightarrow
Isotypical_representation
Local government in some parts of England
In England, a unitary authority or unitary council is a type of local authority that performs all local government functions, in contrast to the two-tier
Unitary authorities of England
Unitary_authorities_of_England
Operator in quantum field theory
invariant. For every irreducible unitary representation of L k {\displaystyle L_{k}} there is an irreducible unitary representation of the full Poincaré group
Pauli–Lubanski_pseudovector
Axiomatic approach to quantum field theory
{\mathcal {A}}(O_{2})]=0} . Poincaré covariance: A strongly continuous unitary representation U ( P ) {\displaystyle U({\mathcal {P}})} of the Poincaré group
Algebraic quantum field theory
Algebraic_quantum_field_theory
(possibly infinite dimensional) unitary representations. The theorem was first published in 1943. A unitary representation ρ : G → U ( H ) {\displaystyle
Gelfand–Raikov_theorem
Theorem of Fourier transforms of Borel measures
on G {\displaystyle G} , one can construct a strongly continuous unitary representation of G {\displaystyle G} in a natural way: Let F 0 ( G ) {\displaystyle
Bochner's_theorem
K-type is a representation of a maximal compact subgroup K of a semisimple Lie group G that is in some sense the smallest representation of K occurring
Minimal_K-type
Japanese mathematician
homogeneous spaces and the theory of discrete breaking symmetry in unitary representation theory. He has been a member of the Science Council of Japan since
Toshiyuki_Kobayashi
Application of Fourier analysis to non-abelian topological groups
then L2(G) as a unitary representation of G is a direct integral of irreducible representations. It is parametrized therefore by the unitary dual, the set
Noncommutative harmonic analysis
Noncommutative_harmonic_analysis
Result in representation theory
in representation theory, named after Austrian-American mathematician Friederich Mautner, states that if G is a topological group and π a unitary representation
Mautner's_lemma
Projection of spin along the direction of momentum
SE(2) rotation by θ. This is the helicity h representation. There is also another unitary representation which transforms non-trivially under the SE(2)
Helicity_(particle_physics)
Universal construction of a complex Lie group from a real Lie group
representations of the group. In any finite-dimensional faithful unitary representation of the compact group it can be realized concretely as a closed subgroup
Complexification_(Lie_group)
*-algebra of bounded operators on a Hilbert space
if V is any unitary representation of Γ, then, regarding Γ as the diagonal subgroup of Γ × Γ, the corresponding induced representation on l2 (Γ, V) is
Von_Neumann_algebra
German-American mathematician and physicist (1908–1989)
projective unitary representations of Lie groups gives a condition for when a projective unitary representation of a Lie group comes from an ordinary unitary representation
Valentine_Bargmann
Symmetry transformation in particle physics for the strong and weak forces
Since any representation of a compact group is equivalent to a unitary representation, we take T ( ω ) {\displaystyle T(\omega )} to be a unitary matrix
Non-abelian gauge transformation
Non-abelian_gauge_transformation
Branch of mathematics that studies the properties of groups
transformation groups) are the mainstays of differential geometry and unitary representation theory. Certain classification questions that cannot be solved in
Group_theory
irreducible representations appearing in the decomposition of the unitary representation of G on L2(G/K). In this case the commutant of G is generated by
Zonal_spherical_function
Lie group of complex numbers of unit modulus; topologically a circle
groups. A projective unitary representation is a continuous group homomorphism from a group G {\displaystyle G} to the projective unitary group of a Hilbert
Circle_group
Integral transform and linear operator
\qquad {\text{ for }}~ad-bc=\pm 1.} This unitary representation is an example of a principal series representation of SL ( 2 , R ) . {\displaystyle ~{\text{SL}}(2
Hilbert_transform
Relativistic quantum mechanical wave equation
symmetry being gauged must admit an N {\displaystyle N} -dimensional unitary representation acting on the spinors. That is, for every g ∈ G ⊆ U ( N ) {\displaystyle
Dirac_equation
Group of unitary matrices
In mathematics, the unitary group of degree n {\displaystyle n} , denoted U ( n ) {\displaystyle \operatorname {U} (n)} , is the group of n × n {\displaystyle
Unitary_group
Group in mathematical representation theory
existence of the Weil representation can be proven abstractly, as follows. The Heisenberg group has an irreducible unitary representation on a Hilbert space
Metaplectic_group
Rule forbidding the coherence of certain states
elements correspond to observables. A unitary representation of O may be decomposed as the direct sum of irreducible unitary representations of O. Each isotypic
Superselection
Non-tensorial representation of the spin group
_{-}\Delta ^{*}} In particular, note that the representation Δ of the orthochronous spin group is a unitary representation. In general, there are Clebsch–Gordan
Spinor
Topics referred to by the same term
przeciwpancerny wzór 35, a Polish anti-tank rifle (codename "Uruguay") Unitary representation, in group theory Uranium, an element formerly having symbol "Ur"
UR
Representation of a Lie group Representation of a Lie algebra Adjoint representation of a Lie group Adjoint representation of a Lie algebra Unitary representation
List_of_Lie_groups_topics
Abstract structure in mathematics
^{*})=\alpha } . Note that u is a representation, but not a unitary representation. u is equivalent to the unitary representation v = ( α μ γ − 1 μ γ ∗ α ∗ )
Compact_quantum_group
Mathematical transform that expresses a function of time as a function of frequency
procedure describes not only the group structure, but also a standard unitary representation of H1 on a Hilbert space, which we denote by ρ : H1 → B(L2(R)).
Fourier_transform
the fundamental unitary representation U λ {\displaystyle U_{\lambda }} of the Heisenberg group is an irreducible unitary representation of N {\displaystyle
Weil–Brezin_Map
Creating a "larger" Lie algebra from a smaller one, in one of several ways
faithful representation of m. If however U(G) is an admissible set of representatives of a projective unitary representation, i.e. a unitary representation up
Lie_algebra_extension
compactification is intimately connected to the finite-dimensional unitary representation theory of a topological group. The kernel of b consists exactly
Bohr_compactification
Harish-Chandra module of a unique irreducible unitary representation of G. Vogan, Jr., David A. (1987), Unitary Representations of Reductive Lie Groups, Annals
Harish-Chandra_module
Construction in representation theory
irreducible unitary representation of G. Geometric invariants of the orbit translate into algebraic invariants of the corresponding representation. In this
Orbit_method
Basic circuit in quantum computing
be measured (sometimes called "Observed"). Quantum gates describe these unitary transformations, that occur when the system is not being measured. The
Quantum_logic_gate
Algebras arising in harmonic analysis
compact group in terms of unitary representations. Let G {\displaystyle G} be a locally compact group. For any unitary representation π {\displaystyle \pi
Fourier_algebra
Type of business entity
A unitary enterprise (Russian: унитарное предприятие) is a government-owned corporation in Russia and some other post-Soviet states. Unitary enterprises
Unitary_enterprise
American mathematician (born 1951)
algebras and their relations with topology, geometry, with the unitary representation theory of Lie groups, K-theory and index theory. Along with H. Blaine
Jonathan Rosenberg (mathematician)
Jonathan_Rosenberg_(mathematician)
Geometric structure
denotes the group of unitary operators acting on a Hilbert space W . {\displaystyle {\mathbf {W} }.\,} The spin representation κ {\displaystyle \kappa
Spinor_bundle
Russian mathematician (1905–1980)
irreducible unitary representations: for every two elements g , h {\displaystyle g,h} of G {\displaystyle G} there is an irreducible unitary representation ρ {\displaystyle
Dmitrii_Abramovich_Raikov
character of a finite-dimensional representation of a compact group. Suppose that π is an irreducible unitary representation of G on a Hilbert space H. If
Harish-Chandra_character
Group of rotations in 3 dimensions
characteristic of infinite-dimensional unitary representations of SO(3). If Π is an infinite-dimensional unitary representation on a separable Hilbert space, then
3D_rotation_group
Country in Southeast Asia and Oceania
rules limit access to natural resources used for income. Indonesia is a unitary republic with a presidential system under the 1945 Constitution. The five
Indonesia
Mathematical group
Projective unitary group Representations of classical Lie groups Symplectic manifold, Symplectic matrix, Symplectic vector space, Symplectic representation Unitary
Symplectic_group
Basic result in the representation theory of Lie groups
representation is a holomorphic irreducible highest weight representation of G with highest weight λ. Its restriction to K is an irreducible unitary representation
Borel–Weil–Bott_theorem
Device in the representation theory of Lie groups
In mathematics, the unitarian trick (or unitary trick) is a device in the representation theory of Lie groups, introduced by Adolf Hurwitz (1897) for the
Unitarian_trick
Quantum algorithm in computer science
\circ \rho _{A}} of B n {\displaystyle B_{n}} will be unitary. We also wish that our representation will have a straightforward encoding into qubits. Let
Aharonov–Jones–Landau algorithm
Aharonov–Jones–Landau_algorithm
UNITARY REPRESENTATION
UNITARY REPRESENTATION
Girl/Female
Anglo Saxon American English Greek
Unity.
Girl/Female
Hindu, Indian
Unity
Girl/Female
Indian
Amazing
Girl/Female
Indian, Telugu
Unity
Girl/Female
Indian
Unity
Girl/Female
Assamese, Bengali, Hindu, Indian, Kannada, Marathi, Rajasthani, Sanskrit, Sindhi, Traditional
Unity
Girl/Female
Tamil
Unity
Girl/Female
Irish English
Together.
Girl/Female
Hindu
Deeply rooted (Celebrity Names: Akshay Kumar and Twinkle Kumar)
Girl/Female
Bengali, Indian
Unity
Girl/Female
American, Australian, British, Christian, English, Irish
Harmonious; Oneness; Together
Boy/Male
Anglo Saxon
Unity.
Boy/Male
Anglo Saxon American English Latin
Unity.
Boy/Male
Arabic
Unity
Female
English
English name derived from the vocabulary word, UNITY means "oneness, unity."
Girl/Female
African, Australian, British, English, Hindu, Indian
Oneness; Sisterly
Girl/Female
Tamil
Ekta | à®à®•à®¤à®¾, à®à®•à®¤à®¾
Unity
Ekta | à®à®•à®¤à®¾, à®à®•à®¤à®¾
Girl/Female
Indian, Telugu
Unity
Girl/Female
Tamil
Unity
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
A Star; Deep Rooted
UNITARY REPRESENTATION
UNITARY REPRESENTATION
Boy/Male
Hindu
God of the earth
Boy/Male
American, Australian, British, Chinese, Christian, Danish, Dutch, English, French, German, Gothic, Greek, Irish, Italian, Jamaican, Latin, Netherlands, Swedish, Swiss
Conquering; Prevailing; Victorious
Surname or Lastname
English
English : variant of Vassell.
Surname or Lastname
English
English : habitational name from a minor place in Somerset, an area of land in the marshes near Markham. This is first recorded in the form Rodenye; it derives from the genitive case of the Old English personal name Hroda (a short form of the various compound names with the first element hrÅð ‘renown’) + Old English Ä“g ‘island’, ‘dry land (in a fen)’.
Girl/Female
Indian
Mercy
Surname or Lastname
English (chiefly southern)
English (chiefly southern) : topographic name for someone who lived near a road or path, Old English weg (cognate with Old Norse vegr, Old High German weg), or a habitational name from some minor place named with this word, as for example any of the places called Way or Waye, in Devon.
Surname or Lastname
English and Scottish
English and Scottish : habitational name from a place named Barmore or Barmoor, numerous examples of which are found in Derbyshire, North Yorkshire, and Northumberland, as well as the Scottish regions of Angus, Galloway, and Strathclyde. In Britain the surname is now rare and is found only in Manchester.
Boy/Male
Arabic
Servant of the generous one.
Surname or Lastname
English
English : nickname for a refined person, sometimes no doubt given ironically, from Old French, Middle English curteis, co(u)rtois ‘refined’, ‘accomplished’ (a derivative of Old French court, see Court 1).English : from Middle English curt ‘short’ + hose ‘leggings’, hence a nickname for a short person or one who wore short stockings. This nickname was borne by William the Conqueror’s son Robert, but it is not clear whether it has given rise to any surnames.Altered form of French Courtois.
Boy/Male
French
Piper.
UNITARY REPRESENTATION
UNITARY REPRESENTATION
UNITARY REPRESENTATION
UNITARY REPRESENTATION
UNITARY REPRESENTATION
n.
The act of rendering sanitary; the science of sanitary conditions; the preservation of health; the use of sanitary measures; hygiene.
n.
The urinary bladder.
a.
Inflicting punishment; avenging; punitory.
adv.
In an unwary manner.
a.
Of or pertaining to health; designed to secure or preserve health; relating to the preservation or restoration of health; hygienic; as, sanitary regulations. See the Note under Sanatory.
n.
Any definite quantity, or aggregate of quantities or magnitudes taken as one, or for which 1 is made to stand in calculation; thus, in a table of natural sines, the radius of the circle is regarded as unity.
pl.
of Tunicary
pl.
of Notary
n.
Concord; harmony; conjunction; agreement; uniformity; as, a unity of proofs; unity of doctrine.
n.
Unity.
a.
Beneficial, as opposed to statutory or civil; as, bonitary dominion of land.
n.
An advocate of sanitary measures; one especially interested or versed in sanitary measures.
a.
Of or pertaining to the urine; as, the urinary bladder; urinary excretions.
a.
Of or pertaining to a unit or units; relating to unity; as, the unitary method in arithmetic.
n.
a notary or scrivener.
n.
A urinary calculus.
n.
One who records in shorthand what is said or done; as, the notary of an ecclesiastical body.
superl.
Unwary; unready.
a.
Of the nature of a unit; not divided; united.
n.
A public officer who attests or certifies deeds and other writings, or copies of them, usually under his official seal, to make them authentic, especially in foreign countries. His duties chiefly relate to instruments used in commercial transactions, such as protests of negotiable paper, ship's papers in cases of loss, damage, etc. He is generally called a notary public.