Formality in the Deligne-Langlands correspondence

2023/02/21 by Antor, Jonas · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2302.11010

Abstract

The Deligne-Langlands correspondence parametrizes irreducible representations of the affine Hecke algebra H^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 χ of H^aff an equivalence of triangulated categories between a perfect derived category of dg-modules D_perf(H^aff/(ker(χ)) - 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'.

Cited by

• Geometric realizations of affine Hecke algebras with unequal parameters

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