Diamonds and Hecke Algebra Representations

@inproceedings{Brenti2006DiamondsAH,
  title={Diamonds and Hecke Algebra Representations},
  author={Francesco Brenti and Fabrizio Caselli},
  year={2006}
}
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 Kazhdan and Lusztig and contains several new ones. 

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