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Multiplicities and tensor product coefficients for
We apply some recent developments of Baldoni-DeLoera-Vergne on vector
partition functions, to Kostant and Steinberg formulas, in the case of .
We therefore get a fast {\sc Maple} program that computes for : the
multiplicity of the weight in the representation
of highest weight ; the multiplicity
of the representation in . The computation also gives the locally polynomial functions
and
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