Garsia-Haiman modules for hook partitions and Green polynomials with two variables
نویسنده
چکیده
The Garsia-Haiman modules are doubly graded modules for the symmetric groups, introduced by A. Garsia and M. Haiman [GH] to prove Macdonald’s positivity conjecture [M1]. These modules are defined for partitions of positive integers n, denoted by Dμ. The dimension of Dμ is given by n! whenever μ is a partition of n [H2]. As this fact implies, the Garsia-Haiman modules Dμ are isomorphic to the coinvariant algebra Rn of Sn, the left regular representation of Sn. Let Dμ = ⊕ r,sD r,s μ be the homogeneous decomposition of Dμ. In this paper, we concerns with module structures of homogeneous components D μ . For each s, let D∗,s μ = ⊕
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