Weight sum formulae in Lie algebra representations

✍ Scribed by John M. Burns; Michael J. Clancy

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 126 KB
• Volume: 257
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00013-3

✦ Synopsis

Many formulae in the representation theory of Lie algebras involve sums of weights, the most celebrated being that of H. Weyl [Math. Z. 24 (1926) 377-395]. In this note we will derive some elementary, but very useful, formulae for summing subsets of weights of a Lie algebra representation. We also give a selection of applications of these formulae.