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

1998/04/07 by Mark Shimozono, Jerzy Weyman, Shimozono, Mark +1 · 2 citations
Mathematics · #05E05 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/9804036

31 pages, AMS-LaTeX

arxiv created 1998/04/07 · arxiv updated 2009/11/30

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.

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• Representation Theoretic Bases for the Δ-Springer Module
• Weighted K-k-Schur functions and their application to the K-k-Schur alternating conjecture

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