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MIT Combinatorics Seminar

The combinatorics of the Garsia-Haiman modules for hook shapes

Yuval Roichman  (Bar-Ilan University, Israel)

Wednesday, February 21, 2007    4:15 pm    Room 2-136


ABSTRACT

A family of monomial bases of the Garsia-Haiman modules for hook shapes is presented, including k-analogues of the classical descent and Artin bases for the coinvariant algebra of type A. An explicit formula for the S_n-action on the k-th descent basis is given, and combinatorial decomposition rules, which extend a classical result of Lusztig and Stanley, are deduced. Relations with recent works of Haglund, Haiman, and Loehr will be mentioned.

Joint work with Ron Adin and Jeff Remmel.