algebra, a Weyl module is a representation of a reductive algebraic group, introduced by Carter and Lusztig (1974, 1974b) and named after Hermann Weyl. In characteristic 0...

dimension is odd, or it will decompose into a pair of so-called "half-spin" or Weyl representations if the dimension is even. What characterizes spinors and...

it is convenient to choose an inner product that is invariant under the Weyl group, that is, under reflections about the hyperplanes orthogonal to the...

in which they are described as nonartinian simple rings. The module theory for the Weyl algebras is well studied and differs significantly from that of...

Schur–Weyl duality is the statement that the space of two-tensors decomposes into symmetric and antisymmetric parts, each of which is an irreducible module...

the Weyl algebra to differential equations. An (algebraic) D-module is, by definition, a left module over the ring An(K). Examples for D-modules include...

algebra, the Weyl algebras are abstracted from the ring of differential operators with polynomial coefficients. They are named after Hermann Weyl, who introduced...

representations of Lie algebras Theorem of the highest weight Generalized Verma module Weyl module E.g., Hall 2015 Chapter 9 Hall 2015 Section 9.2 Hall 2015 Sections...

quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is...

introduced by Adolf Hurwitz (1897) for the special linear group and by Hermann Weyl for general semisimple groups. It applies to show that the representation...

the characters of Demazure modules, and is a generalization of the Weyl character formula. The dimension of a Demazure module is a polynomial in the highest...

Weyl–Brauer matrices Higher-dimensional gamma matrices Clifford module bundle Atiyah, Michael; Bott, Raoul; Shapiro, Arnold (1964), "Clifford Modules"...

Weyl group Weyl integral Weyl integration formula Weyl law Weyl metrics Weyl module Weyl notation Weyl quantization Weyl relations Weyl scalar Weyl semimetal...

a Jantzen filtration is a filtration of a Verma module of a semisimple Lie algebra, or a Weyl module of a reductive algebraic group of positive characteristic...

of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms of linear maps. The module construction...

case of the splitting of a module for a semisimple Lie group into its irreducible factors. In dimension 4, the Weyl module decomposes further into a pair...

(In the positive characteristic case, the construction only produces Weyl modules, which may not be irreducible.) branching branching rule Brauer Brauer's...

theory, "semi-simplicity" is also called complete reducibility. For example, Weyl's theorem on complete reducibility says a finite-dimensional representation...

was worked out mainly by E. Cartan and H. Weyl and because of that, the theory is also known as the Cartan–Weyl theory. The theory gives the structural...

ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic...

described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics...

first need to describe the Weyl group action centered at − ρ {\displaystyle -\rho } . For any integral weight λ and w in the Weyl group W, we set w ∗ λ :=...

mathematics, an algebraic character is a formal expression attached to a module in representation theory of semisimple Lie algebras that generalizes the...

}}} where ⋅ {\displaystyle \cdot } is the affine action of the Weyl group. The Verma module M λ {\displaystyle M_{\lambda }} is called singular, if there...

finite Weyl group. For each w ∈ W denote by Mw be the Verma module of highest weight −w(ρ) − ρ where ρ is the half-sum of positive roots (or Weyl vector)...

suitable space of functions on G, with G acting by translation. See Peter–Weyl theorem for the compact case. If G is a Lie group but not compact nor abelian...

In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group G in terms of a maximal...

construction using Verma modules. In Weyl's approach, the construction is based on the Peter–Weyl theorem and an analytic proof of the Weyl character formula...

finite-dimensional module over g {\displaystyle {\mathfrak {g}}} is semisimple as a module (i.e., a direct sum of simple modules.) Weyl's theorem implies...

product Schur product theorem Schur test Schur's property Schur's theorem Schur's number Schur–Horn theorem Schur–Weyl duality Schur–Zassenhaus theorem...