• 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...
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    Spinor (redirect from Majorana-Weyl spinor)
    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...
    72 KB (9,924 words) - 15:56, 26 May 2025
  • 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...
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  • 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...
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  • 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...
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  • 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...
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  • algebra, the Weyl algebras are abstracted from the ring of differential operators with polynomial coefficients. They are named after Hermann Weyl, who introduced...
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    quantum field theory, the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles called Weyl fermions. The equation is...
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  • 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...
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  • 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...
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  • 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...
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  • Weyl–Brauer matrices Higher-dimensional gamma matrices Clifford module bundle Atiyah, Michael; Bott, Raoul; Shapiro, Arnold (1964), "Clifford Modules"...
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  • 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...
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  • Weyl group Weyl integral Weyl integration formula Weyl law Weyl metrics Weyl module Weyl notation Weyl quantization Weyl relations Weyl scalar Weyl semimetal...
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  • theory, "semi-simplicity" is also called complete reducibility. For example, Weyl's theorem on complete reducibility says a finite-dimensional representation...
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  • 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...
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  • 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...
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  • (In the positive characteristic case, the construction only produces Weyl modules, which may not be irreducible.) branching branching rule Brauer Brauer's...
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  • ring which has a faithful simple left module. Well known examples include endomorphism rings of vector spaces and Weyl algebras over fields of characteristic...
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  • 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 :=...
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    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...
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    described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics...
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  • mathematics, an algebraic character is a formal expression attached to a module in representation theory of semisimple Lie algebras that generalizes the...
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  • subalgebra h {\displaystyle {\mathfrak {h}}} that are invariant under the Weyl group W {\displaystyle W} . Let g {\displaystyle {\mathfrak {g}}} be a semisimple...
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  • 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...
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    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...
    30 KB (4,472 words) - 20:43, 23 November 2024
  • product Schur product theorem Schur test Schur's property Schur's theorem Schur's number Schur–Horn theorem Schur–Weyl duality Schur–Zassenhaus theorem...
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  • 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)...
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  • 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...
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  • is r. Given a right module M over the Weyl algebra A n {\displaystyle A_{n}} , the Gelfand–Kirillov dimension of M over the Weyl algebra coincides with...
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