The combinatorics of the Garsia-Haiman modules for hook shapes (extended abstract)

Ron M. Adin, Jeffrey B. Remmel, Yuval Roichman

Research output: Contribution to conferencePaperpeer-review

Abstract

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 exhibit algebraic decompositions of the Garsia-Haiman modules for hook shapes that correspond to the combinatorial interpretation of the modified Macdonald polynomial that has recently been proved by Haglund, Haiman, and Loehr [20, 21].

Original languageEnglish
StatePublished - 2007
Event19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China
Duration: 2 Jul 20076 Jul 2007

Conference

Conference19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07
Country/TerritoryChina
CityTianjin
Period2/07/076/07/07

Keywords

  • Descent basis
  • Garsia-Haiman module
  • Solomon descent representation

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