Nonsplit Hecke algebras and perverse sheaves

• G. Lusztig ^[1]
  1. [1] M.I.T., Cambridge
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 4 (Special Issue: The Mathematics of Joseph Bernstein), 2016, págs. 1953-1986
• Idioma: inglés
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• Resumen

  • Let H be a Hecke algebra arising as an endomorphism algebra of the representation of a Chevalley group G over Fq 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 B4 and that of L is of type B2.