The Combinatorics of the Garsia-Haiman Modules for Hook Shapes

Details The Combinatorics of the Garsia-Haiman Modules for Hook Shapes The Combinatorics of the Garsia-Haiman Modules for Hook Shapes

2007-03-11

arxiv.org/abs/math/0703308v1

Mathematics

Representation Theory

34 pages; 7 figures

Scientific paper

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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