Vector partition function and representation theory

2005/06/09 by Charles Cochet, Cochet, Charles
Chemistry · Mathematics · #52B55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Primary 22E46 #Representation Theory (math.RT) #math.CO #math.RT #msc:22E46 #msc:52B55

paper · pdf · doi:10.48550/arxiv.math/0506159

Accepted for software demonstration during FPSAC 2005 (Taormina, Italy). 12 pages

arxiv created 2005/06/09 · openalex publication_date 2005/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Nested sets and Jeffrey Kirwan cycles

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