Representations of Coxeter groups and Hecke algebras

@article{Kazhdan1979RepresentationsOC,
  title={Representations of Coxeter groups and Hecke algebras},
  author={D. Kazhdan and G. Lusztig},
  journal={Inventiones mathematicae},
  year={1979},
  volume={53},
  pages={165-184}
}
here l(w) is the length of w. In the case where Wis a Weyl group and q is specialized to a fixed prime power, | ~ can be interpreted as the algebra of intertwining operators of the space of functions on the flag manifold of the corresponding finite Chevalley group G(Fq) (see [loc. cit., Ex. 24]). Therefore, the problem of decomposing this space of functions into irreducible representations of G(Fq) is equivalent to the problem of decomposing the regular representation o f ~ | (12. It is known… Expand
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