Dept. Math, Hokkaido Univ. EPrints Server

Garsia-Haiman modules for hook partitions and Green polynomials with two variables

Preprint Series # 820
Morita, Hideaki Garsia-Haiman modules for hook partitions and Green polynomials with two variables. (2006);

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Abstract

We consider Garsia-Haiman modules for the symmetric groups, a doubly graded generalization of Springer modules. Our main interest lies in singly graded submodules of a Garsia-Haiman module. We show that these submodules satisfy a certain combinatorial property, and verify that this property is implied by a behavior of Macdonald polynomials at roots of unity.

Item Type:Preprint
Additional Information:60
Uncontrolled Keywords:Symmetric groups, Garsia-Haiman modules, Green polynomials with two variables, Macdonald polynomials, Roots of unity
Subjects:20-xx GROUP THEORY AND GENERALIZATIONS
05-xx COMBINATORICS
ID Code:1653