22054 articles – 15889 references  [version française]
 HAL: hal-00000431, version 1
 arXiv: math.CO/0306308
 Multiplicities and tensor product coefficients for $A_r$
 (2003-06-20)
 We apply some recent developments ofBaldoni-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 $c_{\lambda,\mu,\nu}$.
 1: Institut de Mathématiques de Jussieu (IMJ) CNRS : UMR7586 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot
 Subject : Mathematics/CombinatoricsMathematics/Representation Theory
 Keyword(s): Kostant partition functions – polytope – number of integral points – weight multiplicities for $A_r$ – tensor product coefficients – Steinberg formula
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 hal-00000431, version 1 http://hal.archives-ouvertes.fr/hal-00000431 oai:hal.archives-ouvertes.fr:hal-00000431 From: Charles Cochet <> Submitted on: Friday, 20 June 2003 16:33:39 Updated on: Friday, 20 June 2003 16:34:48