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Journal Articles Documenta Mathematica Year : 2015

Linear Koszul duality and Fourier transform for convolution algebras

Abstract

In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in K-homology defined in a previous paper and the Fourier transform isomorphism for convolution algebras in Borel-Moore homology are related by the Chern character. So, Koszul duality appears as a categorical upgrade of Fourier transform of constructible sheaves. This result explains the connection between the categorification of the Iwahori-Matsumoto involution for graded affine Hecke algebras (due to Evens and the first author) and for usual affine Hecke algebras (obtained in a previous paper).
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Dates and versions

hal-00937414 , version 1 (28-01-2014)
hal-00937414 , version 2 (20-05-2015)
hal-00937414 , version 3 (14-09-2015)

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Ivan Mirkovic, Simon Riche. Linear Koszul duality and Fourier transform for convolution algebras. Documenta Mathematica, 2015, 20, pp.989-1038. ⟨hal-00937414v3⟩
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