Weight sum formulae in Lie algebra representations

Johns M. Burns; Michael J. Clancy

doi:10.1016/S0021-8693(02)00013-3

Weight sum formulae in Lie algebra representations

Johns M. Burns, Michael J. Clancy

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Journal of Algebra
Volume	257
Issue number	1
DOIs	https://doi.org/10.1016/S0021-8693(02)00013-3
Publication status	Published - 1 Nov 2002
Externally published	Yes

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AB - 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.

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Weight sum formulae in Lie algebra representations

Abstract

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