Vector partition function and representation theory

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.

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

References in corpus (5)

• Toric reduction and a conjecture of Batyrev and Materov
• Residues formulae for volumes and Ehrhart polynomials of convex polytopes
• A vector partition function for the multiplicities of sl_k(C)
• Nested sets and Jeffrey Kirwan cycles
• On the Computation of Clebsch-Gordan Coefficients and the Dilation Effect

Cited by in corpus (7)

• Applications of Equivariant Cohomology
• Zonotopal algebra and forward exchange matroids
• Computation of Dilated Kronecker Coefficients
• Multiplicity of compact group representations and applications to Kronecker coefficients
• Multiplicity formulas for fundamental strings of representations of classical Lie algebras
• The $q$-analog of Kostant's partition function and the highest root of the classical Lie algebras
• Weight multiplicity formulas for bivariate representations of classical Lie algebras