Abstract
Let H be a Hecke algebra arising as an endomorphism algebra of the representation of a Chevalley group G over \(F_{q}\) induced by a unipotent cuspidal representation of a Levi quotient L of a parabolic subgroup. We assume that L is not a torus. In this paper we outline a geometric interpretation of the coefficients of the canonical basis of H in terms of perverse sheaves. We illustrate this in detail in the case where the Weyl group of G is ot type \(B_{4}\) and that of L is of type \(B_{2}\).
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Dedicated to Joseph Bernstein for his 70-th birthday
Supported in part by National Science Foundation Grant DMS-1303060 and by a Simons Fellowship.
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Lusztig, G. Nonsplit Hecke algebras and perverse sheaves. Sel. Math. New Ser. 22, 1953–1986 (2016). https://doi.org/10.1007/s00029-016-0272-8
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DOI: https://doi.org/10.1007/s00029-016-0272-8