Multi-atoms and monotonicity of generalized Kostka polynomials
Quantum Algebra
2007-05-23 v1 Combinatorics
Abstract
The generalized Kostka polynomials are the Poincare polynomials of isotypic components of certain graded GL(n)-modules. The former satisfy a monotonicity property arising from natural surjections of the corresponding modules. This monotonicity property is realized combinatorially by a directed system of order- and statistic-preserving embeddings between the sets of Littlewood-Richardson (LR) tableaux that describe the generalized Kostka polynomials. Each set of LR tableaux is embedded into a cocyclage poset of column-strict tableaux of a fixed content, and the image is characterized in terms of catabolizable tableaux.
Cite
@article{arxiv.math/9804038,
title = {Multi-atoms and monotonicity of generalized Kostka polynomials},
author = {Mark Shimozono},
journal= {arXiv preprint arXiv:math/9804038},
year = {2007}
}
Comments
22 pages, AMS-LaTeX