|MIT Combinatorics Seminar
The combinatorics of the Garsia-Haiman modules for hook shapes
(Bar-Ilan University, Israel)
Wednesday, February 21, 2007
4:15 pm Room 2-136
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.