Graded characters of modules supported in the closure of a nilpotent conjugacy class

Details Graded characters of modules supported in the closure of a nilpotent conjugacy class Graded characters of modules supported in the closure of a nilpotent conjugacy class

1998-04-07

arxiv.org/abs/math/9804036v1

Mathematics

Quantum Algebra

31 pages, AMS-LaTeX

Scientific paper

We study the Poincare polynomials of isotypic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials generalize the Kostka-Foulkes and are q-analogues of Littlewood-Richardson coefficients corresponding to arbitrary tensor products of irreducibles. Many properties and formulas for these polynomials are derived, such as a generalized Morris recurrence, q-Kostant formula, and a conjectural formula in terms of catabolizable tableaux and charge.

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