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A duality between -multiplicities in tensor products and -multiplicities of weights for the root systems or
Starting from Jacobi-Trudi's type determinental expressions for the Schur
functions corresponding to types and we define a natural
-analogue of the multiplicity when is a
tensor product of row or column shaped modules defined by . We prove that
these -multiplicities are equal to certain Kostka-Foulkes polynomials
related to the root systems or . Finally we derive formulas expressing
the associated multiplicities in terms of Kostka numbers
On the complement of the Richardson orbit
We consider parabolic subgroups of a general algebraic group over an
algebraically closed field whose Levi part has exactly factors. By a
classical theorem of Richardson, the nilradical of a parabolic subgroup has
an open dense -orbit. In the complement to this dense orbit, there are
infinitely many orbits as soon as the number of factors in the Levi part is
. In this paper, we describe the irreducible components of the
complement. In particular, we show that there are at most irreducible
components.Comment: 15 page
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