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### Kostka numbers and tensor product coefficients in A_r via polytopes.

Algebra & Discrete Mathematics

 Speaker: Charles Cochet, Universit{\'e} Paris 7, France Location: 693 Kerr Start time: Fri, Jan 9 2004, 12:10PM

We apply some recent developments of Baldoni-Vergne and Baldoni-DeLoera-Vergne on vector partition functions, to Kostant's and Steinberg's formulas, in the case of the Lie algebra $A_r$. We therefore get a fast {\sc Maple} program that computes for $A_r$: the Kostka number, that is the multiplicity of a weight in a finite-dimensional irreducible representation; the Littlewood-Richardson coefficients, that is the coefficients of the decomposition of the tensor product of two finite-dimensional irreducible representations.