Multiplicities and tensor product coefficients for A_r

2003/06/20 by Charles Cochet, Cochet, Charles
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #combinatorics #computer algebra #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.math/0306308

arxiv created 2003/06/20 · openalex publication_date 2003/06/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply some recent developments of Baldoni-DeLoera-Vergne on vector partition functions, to Kostant and Steinberg formulas, in the case of A_r. We therefore get a fast \sc Maple program that computes for A_r: the multiplicity c_λ,μ of the weight μ in the representation V(λ) of highest weight λ; the multiplicity c_λ,μ,ν of the representation V(ν) in V(λ)⊗ V(μ). The computation also gives the locally polynomial functions c_λ,μ and c_λ,μ,ν.

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