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equivariant Artin L-function is a function associated to a finite Galois extension of global fields created by packaging together the various Artin L-functions
Equivariant_L-function
Type of Dirichlet series associated to number field extensions
Hilbert's twelfth problem. Equivariant L-function Perlis 2001. Martinet 1977, p. 18. Artin, E. (1923). "Über eine neue Art von L Reihen". Hamb. Math. Abh
Artin_L-function
Subfield of number theory
In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula
Special_values_of_L-functions
Generalization of the Riemann zeta function for algebraic number fields
Society, pp. 517–525, ISBN 978-0-8218-1635-6 Flach, Mathias (2004), "The equivariant Tamagawa number conjecture: a survey", in Burns, David; Popescu, Christian;
Dedekind_zeta_function
estimates to change in appropriate ways with such transformations. The term equivariant estimator is used in formal mathematical contexts that include a precise
Invariant_estimator
Interatomic potentials constructed by machine learning programs
significant limitation of early MPNNs was that they were not inherently equivariant to rotations and reflections of atomic structures — meaning predictions
Machine-learned interatomic potential
Machine-learned_interatomic_potential
Class of artificial neural networks
their nodes, GNN architectures are commonly designed to be permutation equivariant: reordering the nodes in the input reorders the corresponding node representations
Graph_neural_network
ramify in K/k. The S-imprimitive equivariant Artin L-function θ(s) is obtained from the usual equivariant Artin L-function by removing the Euler factors
Brumer–Stark_conjecture
Branch of mathematics that studies abstract algebraic structures
and ψ {\displaystyle \psi } of a group G {\displaystyle G} , then an equivariant map from V {\displaystyle V} to W {\displaystyle W} is a linear map α
Representation_theory
counterpart of equivariant cohomology. For example, Borel's theorem states that the cohomology ring of a classifying stack is a polynomial ring. l-adic sheaf
Cohomology_of_a_stack
Machine learning technique
\mathbb {R} ^{m\times n}} an arbitrary matrix. The softmax function is permutation equivariant in the sense that: softmax ( A D B ) = A softmax ( D ) B
Attention_(machine_learning)
previous position: that is, for every integer i, yi = xi − 1. A function f is equivariant under the shift map if the transformation on configurations described
Curtis–Hedlund–Lyndon_theorem
trees are Fn-equivariantly isometric. Hence the map T ↦ ℓ T {\displaystyle T\mapsto \ell _{T}} from Xn to the set of R-valued functions on Fn is injective
Outer_space_(mathematics)
Covariance and correlation
space to kernel space. Cross-correlation is equivariant to translation; kernel cross-correlation is equivariant to any affine transforms, including translation
Cross-correlation
Differential operator in mathematics
{\displaystyle 0} ) and then applying the ordinary Laplacian. The Laplacian is equivariant under pullback by every Euclidean transformation. More precisely, if
Laplace_operator
This is usually done by means of intersection theory. Epidemiology Equivariant noncommutative algebraic geometry Ergodic Ramsey theory a branch where
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Romanian-American mathematician
formulated equivariant versions of Iwasawa's main conjecture over function fields and number fields, proving unconditionally the function field version
Cristian_Dumitru_Popescu
Concept in mathematics
{\displaystyle P\times ^{G}W} over M is isomorphic to the space of G-equivariant W-valued functions on P. More generally, the space of k-forms with values in P
Connection_(principal_bundle)
American mathematician
characterizing cellular automata as being defined by continuous equivariant functions on a shift space. Curtis was the author of two books, Matrix Groups
Morton_L._Curtis
Theorem that any three objects in space can be simultaneously bisected by a plane
attributed there to Stefan Banach, for the n = 3 case. In the field of Equivariant topology, this proof would fall under the configuration-space/tests-map
Ham_sandwich_theorem
Type of polynomial sequence
defined is shift-equivariant; such a Q is then a delta operator. Here, we define a linear operator Q on polynomials to be shift-equivariant if, whenever f(x)
Sheffer_sequence
Process of extending a representation of a subgroup to the parent group
and ρ of G, the space of H-equivariant linear maps from σ to Res(ρ) has the same dimension over K as that of G-equivariant linear maps from Ind(σ) to
Induced_representation
Belgian mathematician
important results on the l-adic representations attached to modular forms, and the conjectural functional equations of L-functions. Deligne also focused
Pierre_Deligne
Branch of mathematics
Chern character is used in the Hirzebruch–Riemann–Roch theorem. The equivariant algebraic K-theory is an algebraic K-theory associated to the category
K-theory
Type of artificial neural network
However, many other properties are instead equivariant. The volume of a cat changes when it is scaled. Equivariant properties such as a spatial relationship
Capsule_neural_network
Type of feedforward neural network
kernels or filters that slide along input features and provide translation-equivariant responses known as feature maps. Counter-intuitively, most convolutional
Convolutional_neural_network
Fiber bundle whose fibers are group torsors
that the equivariant local trivializations of a principal bundle are in one-to-one correspondence with local sections. Given an equivariant local trivialization
Principal_bundle
Method of estimating the parameters of a statistical model, given observations
gives a real-valued function, L n ( θ ) = L n ( θ ; y ) = f n ( y ; θ ) , {\displaystyle {\mathcal {L}}_{n}(\theta )={\mathcal {L}}_{n}(\theta ;\mathbf
Maximum_likelihood_estimation
) {\displaystyle H=\operatorname {End} _{G}(V)} is the algebra of G-equivariant endomorphisms of V. For each irreducible representation W {\displaystyle
Hecke algebra of a finite group
Hecke_algebra_of_a_finite_group
Mathematical group of loops in a Lie group
twisted equivariant K-theory, and this construction is one of the ingredients in their identification of the Verlinde ring with twisted equivariant K-theory
Loop_group
Ring homomorphism from the cobordism ring of manifolds to another ring
2}{2G_{2k}(\tau )z^{2k} \over (2k)!}\right)} where σL is the Weierstrass sigma function for the lattice L, and G is a multiple of an Eisenstein series. The
Genus of a multiplicative sequence
Genus_of_a_multiplicative_sequence
Conjecture linking two mathematical areas
}})\to K_{*}(C_{r}^{*}(\Gamma )),} called the assembly map, from the equivariant K-homology with Γ {\displaystyle \Gamma } -compact supports of the classifying
Baum–Connes_conjecture
British-Lebanese mathematician (1929–2019)
(discrete series representations), Graeme Segal (equivariant K-theory), Alexander Shapiro (Clifford algebras), L. Smith (homotopy groups of spheres), Paul Sutcliffe
Michael_Atiyah
Type of singular integral operator
The final transformation property asserts that the Riesz transform is equivariant with respect to these two actions; that is, ρ ∗ R j [ ( ρ − 1 ) ∗ f ]
Riesz_transform
Transformations induced by a mathematical group
X to Y is a function f : X → Y such that f(g⋅x) = g⋅f(x) for all g in G and all x in X. Morphisms of G-sets are also called equivariant maps or G-maps
Group_action
Formalism for Thom class representation in differential geometry
Varghese; Quillen, Daniel (1986), "Superconnections, Thom classes, and equivariant differential forms", Topology, 25 (1): 85–110, doi:10.1016/0040-9383(86)90007-8
Mathai–Quillen_formalism
though it has had heuristic value over many years. Now a sophisticated equivariant Tamagawa number conjecture is a major research problem. Tate conjecture
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Left-invariant (or right-invariant) measure on locally compact topological group
a location parameter results in the Pitman estimator, which is best equivariant. When left and right Haar measures differ, the right measure is usually
Haar_measure
Embedding of categories into functor categories
between such functors is the same thing as an equivariant map between G {\displaystyle G} -sets: a set function α : X → Y {\displaystyle \alpha \colon X\to
Yoneda_lemma
Theorem on extension of bounded linear functionals
ISBN 978-1-4612-7155-0. OCLC 840278135. Schmitt, Lothar M (1992). "An Equivariant Version of the Hahn–Banach Theorem". Houston J. Of Math. 18: 429–447
Hahn–Banach_theorem
Manifold upon which it is possible to perform calculus
is useful because tensor fields on M can be regarded as equivariant vector-valued functions on F(M). On a manifold that is sufficiently smooth, various
Differentiable_manifold
Branch of mathematics
Mathématique de France 90 (1962), p. 323-448, numdam Zoran Škoda, Some equivariant constructions in noncommutative algebraic geometry, Georgian Mathematical
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Group homomorphism into the general linear group over a vector space
two representations ρ : G → GL(V) and π : G → GL(W) (also called an equivariant map) is a linear map α : V → W such that α ∘ ρ ( g ) = π ( g ) ∘ α .
Group_representation
Architectural motif in neural networks for aggregating information
{A} )} where GNN {\displaystyle {\text{GNN}}} is a generic permutation equivariant GNN layer (e.g., GCN, GAT, MPNN). The Self-attention pooling layer can
Pooling_layer
Concept in algebraic geometry
] {\displaystyle X=[Y/G]} , the Chow group of X is the same as the G-equivariant Chow group of Y. A key difference from the theory of Chow groups of a
Chow_group_of_a_stack
German mathematician
motives – Matthias Flach and D. Burns, King's College London On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II. (2006) – Burns
Matthias Flach (mathematician)
Matthias_Flach_(mathematician)
Fiber bundle
That is, between any two constructions, there is a G {\displaystyle G} -equivariant bundle isomorphism. This is also called a gauge transformation. This
Associated_bundle
Middle quantile of a data set or probability distribution
-x_{n}\right\|_{2}} In contrast to the marginal median, the geometric median is equivariant with respect to Euclidean similarity transformations such as translations
Median
algebra of a Lie algebra. category of representations Representations and equivariant maps between them form a category of representations. character 1. A
Glossary of representation theory
Glossary_of_representation_theory
Theorem in statistics
{X_{(n)}}{1+k}}} The model is a scale model. Optimal equivariant estimators can then be derived for loss functions that are invariant. Basu's theorem Completeness
Lehmann–Scheffé_theorem
Complex-valued smooth functions of the upper half plane (harmonic analysis topic)
smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup Γ {\displaystyle \Gamma } of S L 2 (
Maass_wave_form
annulus: For an annulus I × T, the extension map to T2 is by construction equivariant with respect to rotations in the second variable, R t f ( x , y ) = f
Sobolev spaces for planar domains
Sobolev_spaces_for_planar_domains
last nonzero term is the tangent sheaf, is called the Euler sequence. equivariant intersection theory See Chapter II of http://www.math.ubc.ca/~behrend/cet
Glossary of algebraic geometry
Glossary_of_algebraic_geometry
Statistical theorem
{X_{(n)}}{1+k}}} The model is a scale model. Optimal equivariant estimators can then be derived for loss functions that are invariant. Basu's theorem — Another
Rao–Blackwell_theorem
Artificial intelligence program by DeepMind
abstract (December 2020) The structure module is stated to use a "3-d equivariant transformer architecture" (John Jumper et al. (1 December 2020), AlphaFold
AlphaFold
Branch of mathematics
Mathematics portal Characterizations of the category of topological spaces Equivariant topology List of algebraic topology topics List of examples in general
Topology
Mathematical arithmetic dynamics function
1007/BF01197321. S2CID 122514918. Ferraguti, Andrea; Micheli, Giacomo (2020). "An equivariant isomorphism theorem for mod p {\displaystyle {\mathfrak {p}}} reductions
Arboreal Galois representation
Arboreal_Galois_representation
Molecule-specific coordinate bonding area in biological systems
PMID 27796788. S2CID 6705144. Sestak F, Schneckenreiter L, Hochreiter S, Mayr A, Klambauer G. "VN-EGNN: Equivariant Graph Neural Networks with Virtual Nodes Enhance
Binding_site
Symplectic topology tool
This approach was the basis of Manolescu's 2013 construction of Pin (2)-equivariant Seiberg–Witten Floer homology, with which he disproved the Triangulation
Floer_homology
Type of integrable system
\chi } is equivariant with respect to the G m {\displaystyle \mathbb {G} _{m}} -actions. Therefore, given any line bundle L {\displaystyle L} on our curve
Hitchin_system
Phenomenon in decision theory and estimation theory
best linear unbiased estimation, least squares estimation and optimal equivariant estimation, all result in the "ordinary" estimator. Yet, as discussed
Stein's_example
Mathematical result in differential geometry
with the elliptic operator, then one replaces ordinary K-theory with equivariant K-theory. Moreover, one gets generalizations of the Lefschetz fixed-point
Atiyah–Singer_index_theorem
Dutch mathematician (1942–2010)
formula, which will later be placed in the more general framework of equivariant cohomology, independently by Berline and Vergne and by Atiyah and Bott
Hans_Duistermaat
Algebraic object with geometric applications
{\text{GL}}(W)} ). Then a tensor of type ρ {\displaystyle \rho } is an equivariant map T : F → W {\displaystyle T:F\to W} . Equivariance here means that
Tensor
Straight path on a curved surface or a Riemannian manifold
deleted tangent bundle TM \ {0}) it is enough that the connection be equivariant under positive rescalings, that is, it is enough that, if w ∈ T x M {\displaystyle
Geodesic
Point minimizing sum of distances to given points
unique whenever the points are not collinear. The geometric median is equivariant for Euclidean similarity transformations, including translation and rotation
Geometric_median
Concept in algebraic geometry
1980s the theory developed interactions with symplectic geometry and equivariant topology, and was used to construct moduli spaces of objects in differential
Geometric_invariant_theory
Expression that may be integrated over a region
differential forms Complex differential form Vector-valued differential form Equivariant differential form Calculus on Manifolds Multilinear form Polynomial differential
Differential_form
Concept in differential geometry
{\displaystyle (M,g)} with an oriented vector bundle E {\displaystyle E} is an equivariant lift of the orthonormal frame bundle P SO ( E ) → M {\displaystyle P_{\operatorname
Spin_structure
Principal bundle associated to a vector bundle
{\displaystyle M} together with a G {\displaystyle G} -equivariant bundle map F G ( M ) → F G L ( M ) {\displaystyle {\mathrm {F} }_{G}(M)\to {\mathrm
Frame_bundle
Swiss physicist and mathematician
Oct 25, 2013. "Giovanni Felder - Elliptic quantum groups and elliptic equivariant cohomology". YouTube. Institut des Hautes Études Scientifiques (IHES)
Giovanni_Felder
mathematics, a Cannon–Thurston map is any of a number of continuous group-equivariant maps between the boundaries of two hyperbolic metric spaces extending
Cannon–Thurston_map
Basic result in the representation theory of Lie groups
G-equivariant holomorphic line bundle Lλ on X and the group G acts on its space of global sections, Γ ( G / B , L λ ) . {\displaystyle \Gamma (G/B,L_{\lambda
Borel–Weil–Bott_theorem
Algebro-geometric stability condition
where n = dim X {\displaystyle n=\dim X} . This can be seen using an equivariant Riemann-Roch theorem. Recall that the Hilbert polynomial P ( k ) {\displaystyle
K-stability
section. Its universal representative is obtained using the machinery of equivariant differential forms.[citation needed] Mathai was awarded the Australian
Varghese_Mathai
Locally constant sheaf of abelian groups on topological space
deck-transform-invariant sections of L _ {\displaystyle {\underline {L}}} gives a local system on X. Similarly, the deck-transform-ρ-equivariant sections give another
Local_system
Statistical measure
scale equivariant and rotation invariant measure that doesn't go to zero for dependent variables. One interpretation of the characteristic function definition
Distance_correlation
Representations of finite groups, particularly on vector spaces
or an equivariant map. The kernel, the image and the cokernel of T {\displaystyle T} are defined by default. The composition of equivariant maps is
Representation theory of finite groups
Representation_theory_of_finite_groups
\mathrm {ad} P} are in one-to-one correspondence with horizontal, G-equivariant Lie algebra-valued forms on P. A prime example is the curvature of any
Adjoint_bundle
Topological invariant of manifolds that can distinguish homotopy-equivalent manifolds
-M.; Zhang, W. (1994-03-01), "Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle", Geometric & Functional Analysis
Analytic_torsion
Subspace defined by a polynomial of degree 2 over a field
{OGr} _{+}(m+1,2m+2)} .) To explain the name: the smallest SO(2m + 1)-equivariant projective embedding of W lands in projective space of dimension 2 m
Quadric_(algebraic_geometry)
Graduate-level textbooks in mathematics
Values of Rankin-Selberg L-Functions Günter Harder, A. Raghuram 2019-12-03 240 9780691197890 204 Introductory Lectures on Equivariant Cohomology Loring W.
Annals_of_Mathematics_Studies
Periodic solution to the n-body problem
groups. The second part of their study involves the development of the equivariant fundamental group, which is employed to identify the topology of the
N-body_choreography
Concept on molecular modeling
many-body expansion of the total potential energy with rotationally equivariant representations of the system. ANI (Artificial Narrow Intelligence) is
Force_field_(chemistry)
on F(E). It is not hard to check that this pulled back form is right-equivariant with respect to the natural action of GLk(R) on F(E) × Rk and vanishes
Vector-valued differential form
Vector-valued_differential_form
Framework for multi-scale signal representation
L ~ v 2 = L x 2 L x x + 2 L x L y L x y + L y 2 L y y = 0 {\displaystyle {\tilde {L}}_{v}^{2}=L_{x}^{2}\,L_{xx}+2\,L_{x}\,L_{y}\,L_{xy}+L_{y}^{2}\,L_{yy}=0}
Scale_space
Mathematics timeline
Society. p. ix. ISBN 9780821843284. Manolescu, Ciprian (2016), "Pin(2)-equivariant Seiberg–Witten Floer homology and the Triangulation Conjecture", Journal
Timeline_of_manifolds
Study of vector bundles, principal bundles, and fibre bundles
structures, spurring the development of infinite-dimensional moment maps, equivariant Morse theory, and relations between gauge theory and algebraic geometry
Gauge_theory_(mathematics)
Spectroscopic technique
interatomic potential and generative model. Zihan Zou et al.. Using equivariant graph neural networks to predict molecular polarizabilities and Hessian
Raman_spectroscopy
Tools for studying groups based on techniques from algebraic topology
of all G {\displaystyle G} -modules is a category (the morphisms are equivariant group homomorphisms, that is group homomorphisms M {\displaystyle M}
Group_cohomology
Parametrizes complex structures on a surface
map from Teichmüller space to the space of Γ {\displaystyle \Gamma } -equivariant solutions to the Beltrami differential equation. These give rise, via
Teichmüller_space
Part of the mathematical subject of group theory
base-vertex in A. Then G is isomorphic to the group π1(A, v) and there is an equivariant isomorphism between the tree X and the Bass–Serre covering tree A ~ {\displaystyle
Bass–Serre_theory
Algorithms for matrix decomposition
temporal dimensions, e.g. time signals, images, or video, features that are equivariant w.r.t. shifts along these dimensions can be learned by Convolutional
Non-negative matrix factorization
Non-negative_matrix_factorization
Analogs of homology groups for algebraic varieties
quotients in the latter category and thus it is more natural to consider equivariant Chow groups of algebraic spaces. A much more formidable extension is
Chow_group
Mathematical study of invariants under symmetries
1980s the theory developed interactions with symplectic geometry and equivariant topology, and was used to construct moduli spaces of objects in differential
Invariant_theory
mathematician, rector of Jönköping University Megumi Harada, Canadian expert on equivariant symplectic and algebraic geometry Eleonor Harboure (1948–2022), first
List_of_women_in_mathematics
Bulgarian mathematician (1949–2026)
Among his best known mathematical works are "Versal deformations of equivariant vector fields for cases of symmetry of order two and three" (Ph.D. thesis
Emil_Horozov
Algebraic study of differential equations
ISBN 9782705612511. Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. Bibcode:2019ctef
Differential_algebra
Algebraic structure used in topology
cohomology Crystalline cohomology Cyclic cohomology Deligne cohomology Equivariant cohomology Étale cohomology Ext groups Flat cohomology Floer homology
Cohomology
Representation of a group or algebra that is a direct sum of simple representations
which is of independent interest: Lemma—Let p:V → W be a surjective equivariant map between representations. If V is semisimple, then p splits; i.e.
Semisimple_representation
EQUIVARIANT L-FUNCTION
EQUIVARIANT L-FUNCTION
Girl/Female
Assamese, British, Gujarati, Hindu, Indian, Kannada, Malay, Malayalam, Marathi, Mythological, Oriya, Sindhi, Tamil
Like a Goddess; Daughter of Shukraacharya; L
Male
Dutch
, God's judge.
Male
Irish
Irish form of Greek Paulos, PÓL means "small."
Male
Scottish
Scottish form of Latin Paulus, PÀL means "small."
Male
Swedish
Swedish form of Greek Paulos, PÃ…L means "small."
Male
Norwegian
Norwegian variant form of Scandinavian Njal, NJÃ…L means "champion."
Male
French
Masculine form of French Gaëlle, GAËL means "holy and generous."
Boy/Male
Indian
Lord of majesty and generosity
Boy/Male
Muslim
Lord of majesty and generosity
Male
Hungarian
Hungarian form of Roman Latin Cornelius, KORNÉL means "of a horn."
Male
French
French name derived from Latin natalis dies, NOËL means "day of birth."
Boy/Male
Irish
Rooster.
Girl/Female
Indian
Pl of hazz, Fortune, Good l
Male
Irish
Irish Gaelic form of Greek MichaÄ“l, MÃCHEÃL means "who is like God?"
Girl/Female
Muslim
Pl of hazz, Fortune, Good l
Male
French
French form of Greek Ioel (Hebrew Yowel), JOËL means "Jehovah is God" or "to whom Jehovah is God."
Boy/Male
Indian, Sanskrit
Miner; L Digger
Male
French
French form of Hebrew Rephael, RAPHAËL means "healed of God" or "whom God has healed."
Male
Hungarian
Hungarian form of Greek Paulos, PÃL means "small."
Girl/Female
African, Arabic, Australian, Danish, German, Muslim, Pashtun, Swahili
Pure; L; Holy; Clean; Dean
EQUIVARIANT L-FUNCTION
EQUIVARIANT L-FUNCTION
Female
Hawaiian
Hawaiian form of Swiss Heidi, HEIKI means "noble sort."Â
Surname or Lastname
English
English : variant of Hilbert.
Girl/Female
Arabic, Australian, Christian, French, German
Strong in War; Form of Matilda; Might; Power; Battle-mighty
Girl/Female
Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sikh
Friend; Good Behaviour
Girl/Female
Hindu
King of the empire
Girl/Female
Australian, Hindu, Indian
The Last Knowledge of Vedas (Shiva)
Girl/Female
American, Christian, Danish, French, German, Hawaiian, Hebrew, Indian, Swedish
Pleasure
Boy/Male
Australian, Dutch, French, German
Ready for Battle; Noble and Ready
Boy/Male
Indian, Sikh
Humble
Girl/Female
Norse
Wife of Bjorn Buna.
EQUIVARIANT L-FUNCTION
EQUIVARIANT L-FUNCTION
EQUIVARIANT L-FUNCTION
EQUIVARIANT L-FUNCTION
EQUIVARIANT L-FUNCTION
n.
An extension at right angles to the length of a main building, giving to the ground plan a form resembling the letter L; sometimes less properly applied to a narrower, or lower, extension in the direction of the length of the main building; a wing.
L. catechunenus, Gr.
One who is receiving rudimentary instruction in the doctrines of Christianity; a neophyte; in the primitive church, one officially recognized as a Christian, and admitted to instruction preliminary to admission to full membership in the church.
n.
The name of the Greek letter /, /, corresponding with the English letter L, l.
n.
An imperfect enunciation of the letter r, in which it sounds like l.
v. t.
To betray; to show. [L.]
a.
Relating to Casserio (L. Gasserius), the discover of the Gasserian ganglion.
n.
See L.
n.
Any small leguminous plant of the genus Lathyrus, especially L. Nissolia.
n.
A short right-angled pipe fitting, used in connecting two pipes at right angles.
n.
A symbol representing fifty units, as 50, or l.
n.
A weed of the genus Lamium (L. amplexicaule) with deeply crenate leaves.
n.
A large stork of the genus Leptoptilos (formerly Ciconia), esp. the African species (L. crumenifer), which furnishes plumes worn as ornaments. The Asiatic species (L. dubius, or L. argala) is the adjutant. See Adjutant.