The Combinatorics of the Garsia-Haiman Modules for Hook Shapes

2007/03/11 by Ron M. Adin, Adin, Ron M., Jeffrey B. Remmel +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.math/0703308

34 pages; 7 figures

arxiv created 2007/03/11 · arxiv updated 2009/12/01

Abstract

Several bases of the Garsia-Haiman modules for hook shapes are given, as well as combinatorial decomposition rules for these modules. These bases and rules extend the classical ones for the coinvariant algebra of type A. We also give a decomposition of the Garsia-Haiman modules into descent representations.

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