Combinatorics of Minuscule Representations
Publisher: Cambridge University Press
Published: 2013
Language: eng
Number of pages: 330
ISBN-13: 9781107026247
Subjects: Combinatorial analysis; Geometry, algebraic; Lie algebras; Lie groups
Description: "Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights may be regarded as points in Euclidean space, and there is a finite group (called a Weyl group) that acts on the set of weights by linear transformations. The minuscule representations are those for which the Weyl group acts transitively on the weights, and the highest weight of such a representation is called a minuscule weight"--