$\mathbb{Z}/m\mathbb{Z}$-graded Lie algebras and perverse sheaves, III: graded double affine Hecke algebra

Abstract

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 $\mathfrak{g}$ together with a $\mathbb{Z}/m\mathbb{Z}$-grading ${\oplus }_i{\mathfrak{g}}_i$ and a block of $G_{\underline{0}}$-equivariant complexes on the nilpotent cone of ${\mathfrak{g}}_{\underline{1}}$ as introduced in \cite{LY1}, we attach a graded DAHA and construct its action on the direct sum of spiral inductions in that block. This generalizes results of Vasserot \cite{V} and Oblomkov-Yun \cite{OY} which correspond to the case of the principal block.

33 pages

References in corpus (1)

• $Z/m$-graded Lie algebras and perverse sheaves, II

Cited by in corpus (1)

• $Z/m$-graded Lie algebras and perverse sheaves, II