The Combinatorics of the Garsia-Haiman Modules for Hook Shapes - Adin, Ron M.; Remmel, Jeffrey B.; Roichman, Yuval (The Electronic Journal of Combinatorics, 2008)
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.