Multiplicities and tensor product coefficients for $A_r$

Details Multiplicities and tensor product coefficients for $A_r$ Multiplicities and tensor product coefficients for $A_r$

2003-06-20

arxiv.org/abs/math/0306308v1

Mathematics

Combinatorics

Scientific paper

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 $c_{\lambda,\mu,\nu}$.

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