Graded characters of modules supported in the closure of a nilpotent conjugacy class
Quantum Algebra
2007-05-23 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.math/9804036,
title = {Graded characters of modules supported in the closure of a nilpotent conjugacy class},
author = {Mark Shimozono and Jerzy Weyman},
journal= {arXiv preprint arXiv:math/9804036},
year = {2007}
}
Comments
31 pages, AMS-LaTeX