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 language | English |
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State | Published - 2007 |
Event | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: 2 Jul 2007 → 6 Jul 2007 |
Conference
Conference | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 |
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Country/Territory | China |
City | Tianjin |
Period | 2/07/07 → 6/07/07 |
Keywords
- Descent basis
- Garsia-Haiman module
- Solomon descent representation