A class of partially ordered sets called diamonds, that includes all Coxeter groups ordered by Bruhat order, is introduced. It is shown that the definition of Kazhdan-Lusztig polynomials can be generalized to the framework of diamonds, and that they can be used to construct a family of Hecke algebra representations that includes those constructed by Kazdhan and Lusztig and contains several new ones.
F. Caselli, F. Brenti, M. Marietti (2006). Diamonds and Hecke algebra representations. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2006, 1-34 [10.1155/IMRN/2006/29407].
Diamonds and Hecke algebra representations
CASELLI, FABRIZIO;
2006
Abstract
A class of partially ordered sets called diamonds, that includes all Coxeter groups ordered by Bruhat order, is introduced. It is shown that the definition of Kazhdan-Lusztig polynomials can be generalized to the framework of diamonds, and that they can be used to construct a family of Hecke algebra representations that includes those constructed by Kazdhan and Lusztig and contains several new ones.File in questo prodotto:
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