Vector partition function and representation theory

We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector partition function, to Kostant's and Steinberg's formulae, for classical Lie algebras \(A\_r\), \(B\_r\), \(C\_r\), \(D\_r\). We therefore get efficient {\tt Maple} programs that compute for these Lie algebras: the m...

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Bibliographic Details
Published inarXiv.org
Main Author Cochet, Charles
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.06.2005
Subjects
Lie groups
Mathematical analysis
Partitions
Partitions (mathematics)
Representations
Tensors
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Summary:We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector partition function, to Kostant's and Steinberg's formulae, for classical Lie algebras \(A\_r\), \(B\_r\), \(C\_r\), \(D\_r\). We therefore get efficient {\tt Maple} programs that compute for these Lie algebras: the multiplicity of a weight in an irreducible finite-dimensional representation; the decomposition coefficients of the tensor product of two irreducible finite-dimensional representations. These programs can also calculate associated Ehrhart quasipolynomials.
ISSN:2331-8422