Multiplicities and tensor product coefficients for \(A_r\)

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 \(c_{\lambda,\mu}\) of the weight \(\mu\) in the representatio...

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Bibliographic Details
Published inarXiv.org
Main Author Cochet, Charles
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.06.2003
Subjects
Functions (mathematics)
Partitions (mathematics)
Polynomials
Representations
Tensors
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Summary: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 \(c_{\lambda,\mu}\) of the weight \(\mu\) in the representation \(V(\lambda)\) of highest weight \(\lambda\); the multiplicity \(c_{\lambda,\mu,\nu}\) of the representation \(V(\nu)\) in \(V(\lambda)\otimes V(\mu)\). The computation also gives the locally polynomial functions \(c_{\lambda,\mu}\) and \(c_{\lambda,\mu,\nu}\).
ISSN:2331-8422