Weight sum formulae in Lie algebra representations
type: Item
instance of: scholarly article
title: Weight sum formulae in Lie algebra representations
zbMATH Open document ID: 1014.17008
DOI: 10.1016/S0021-8693(02)00013-3
author: John M. Burns
author: Michael J. Clancy
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: This paper gives a number of formulae for summing subsets of weights of finite-dimensional representations of finite-dimensional simple complex Lie algebras. The subsets are usually certain hyperplanes or cones cut out by simple roots, fundamental weights, or coroots. The authors also give three applications of these formulae at the end of the paper.
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 1868051
zbMATH Keywords: subsets of weights of finite-dimensional representations
zbMATH Keywords: simple complex Lie algebras
zbMATH Keywords: hyperplanes
zbMATH Keywords: cones
Wikidata QID: Q115340553
reviewed by: Mark R. Sepanski
MaRDI profile type: Publication
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Q4156946
cites work: Affine root systems and Dedekind's \(\eta\)-function
cites work: On actions of a maximal torus on orbits of highest weight vectors
cites work: The NEF Value and Defect of Homogeneous Line Bundles
cites work: Q4833694
cites work: Q5580319
cites work: Q5658292
cites work: Q3897665
cites work: Nef value of homogeneous line bundles and related vanishing theorems
cites work: Homogeneous vector bundles
cites work: Polar sets as nondegenerate critical submanifolds in symmetric spaces
cites work: Les sous-groupes fermes de rang maximum des groupes de Lie clos
cites work: Totally geodesic submanifolds of symmetric spaces. II
description: scientific article; zbMATH DE number 1868051