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Linear Koszul duality and Fourier transform for convolution algebras
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).Comment: v1: 29 pages; v2: 41 pages, many details added; v3: 42 pages, minor
modifications (final version, to appear in Doc. Math.
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