Affiliation:
1. Mathematical Institute, University of Oxford , Oxford OX2 6GG, UK
Abstract
Abstract
The Deligne-Langlands correspondence parametrizes irreducible representations of the affine Hecke algebra $\mathcal{H}^{\operatorname{aff}}$ by certain perverse sheaves. We show that this can be lifted to an equivalence of triangulated categories. More precisely, we construct for each central character $\chi $ of $\mathcal{H}^{\operatorname{aff}}$ an equivalence of triangulated categories between a perfect derived category of dg-modules $D_{\operatorname{perf}}(\mathcal{H}^{\operatorname{aff}}/(\ker (\chi )) - \operatorname{dgMod})$ and the triangulated category generated by the corresponding perverse sheaves. The main step in this construction is a formality result that we prove for a wide range of ‘Springer sheaves’.
Publisher
Oxford University Press (OUP)