ℤ/����ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra

Abstract

© 2018 American Mathematical Society. In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. More precisely, starting with a simple Lie algebra g together with a ℤ/mℤ-grading ⊕i∈ℤ/mℤ gi and a block of DG0 (gi) as introduced in [J. Represent. Theory 21 (2017), pp. 277-321], we attach a graded DAHA and construct its action on the direct sum of spiral inductions in that block. This generalizes results of Vasserot [Duke Math J. 126 (2005), pp. 251-323] and Oblomkov- Yun [Adv. Math 292 (2016), pp. 601-706] which correspond to the case of the principal block.