semisimple element
111Schubert variety — In mathematics, a Schubert variety is a certain subvariety of a Grassmannian, usually with singular points. Described by means of linear algebra, a typical example consists of the k dimensional subspaces V of an n dimensional vector space W ,… …
112Infinitesimal character — In mathematics, the infinitesimal character of an irreducible representation rho; of a semisimple Lie group G on a vector space V is, roughly speaking, a mapping to scalars that encodes the process of first differentiating and then diagonalizing… …
113Representation theory of SL2(R) — In mathematics, the main results concerning irreducible unitary representations of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish Chandra (1952). Structure of the complexified Lie algebra We choose a… …
114Parabolic induction — In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups. If G is a reductive algebraic group and P=MAN is the Langlands decomposition of a parabolic… …
115Generalized Verma module — Generalized Verma modules are object in the representation theory of Lie algebras, a field in mathematics. They were studied originally by James Lepowsky in seventies. The motivation for their study is that their homomorphisms correspond to… …
116Triple system — In algebra, a triple system is a vector space V over a field F together with a F trilinear map: (cdot,cdot,cdot) colon V imes V imes V o V.The most important examples are Lie triple systems and Jordan triple systems. They were introduced by… …
117Algèbre enveloppante — Pour les articles homonymes, voir Algèbre (homonymie). En mathématiques, on peut construire l algèbre enveloppante d une algèbre de Lie . Il s agit une algèbre unitaire qui permet de rendre compte de la plupart des propriétés de …
118Représentation d'algèbre de Lie — En mathématiques, une représentation d une algèbre de Lie est une façon d écrire cette algèbre comme une algèbre de matrices, ou plus généralement d endomorphismes d un espace vectoriel, avec le crochet de Lie donné par le commutateur. Sommaire 1 …
119Eigenvalues and eigenvectors — For more specific information regarding the eigenvalues and eigenvectors of matrices, see Eigendecomposition of a matrix. In this shear mapping the red arrow changes direction but the blue arrow does not. Therefore the blue arrow is an… …
120Macdonald polynomials — In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal polynomials in several variables, introduced by Macdonald (1987). Macdonald originally associated his polynomials with weights λ of finite root systems and used just …
