Geodesic
Linear Koszul duality and Fourier transform for convolution algebras
Documenta mathematica, Tome 20 (2015), pp. 989-1038
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In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in K-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].
DOI : 10.4171/dm/511
Classification : 16E45, 16S37
Mots-clés : Fourier transform, Koszul duality, affine Hecke algebras 
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     author = {Ivan Mirkovi\'c and Simon Riche},
     title = {Linear {Koszul} duality and {Fourier} transform for convolution algebras},
     journal = {Documenta mathematica},
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     year = {2015},
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Ivan Mirković; Simon Riche. Linear Koszul duality and Fourier transform for convolution algebras. Documenta mathematica, Tome 20 (2015), pp. 989-1038. doi: 10.4171/dm/511

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