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Multi-atoms and monotonicity of generalized Kostka polynomials

Mark Shimozono
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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.

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Mark Shimozono. 1998-04-07. Multi-atoms and monotonicity of generalized Kostka polynomials. https://arxiv.org/abs/math/9804038

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