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The Combinatorics of the Garsia-Haiman Modules for Hook Shapes

Ron M. Adin·Jeffrey B. Remmel·Yuval Roichman
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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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Ron M. Adin, Jeffrey B. Remmel, Yuval Roichman. 2007-03-11. The Combinatorics of the Garsia-Haiman Modules for Hook Shapes. https://arxiv.org/abs/math/0703308

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