JournalsdmVol. 20pp. 989–1038

Linear Koszul duality and Fourier transform for convolution algebras

  • Ivan Mirković

    University of Massachusetts Université Clermont Auvergne Amherst, MA Université Blaise Pascal USA Laboratoire de Mathématiques

  • Simon Riche

    BP 10448 F-63000 Clermont-Ferrand CNRS, UMR 6620, LM F-63178 Aubi`ere, France
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Abstract

In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in -homology of [MR3] and the Fourier transform isomorphism for convolution algebras in Borel–Moore homology of [EM] 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 in [EM] and for ordinary affine Hecke algebras in [MR3].

Cite this article

Ivan Mirković, Simon Riche, Linear Koszul duality and Fourier transform for convolution algebras. Doc. Math. 20 (2015), pp. 989–1038

DOI 10.4171/DM/511