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| HAL: hal-00000431, version 1 |
| arXiv: math.CO/0306308 |
| Detailed view |  Export this paper |
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| Multiplicities and tensor product coefficients for $A_r$ |
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| Charles Cochet 1 |
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| (2003-06-20) |
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| 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 $c_{\lambda,\mu,\nu}$. |
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| 1: | Institut de Mathématiques de Jussieu (IMJ) |
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CNRS : UMR7586 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot |
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| Subject | : | Mathematics/Combinatorics Mathematics/Representation Theory |
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| 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 | |
