Geodesic
Linear Koszul duality and Fourier transform for convolution algebras
Documenta mathematica, Tome 20 (2015), pp. 989-1038.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in $K$-homology of citeMR3 and the Fourier transform isomorphism for convolution algebras in Borel--Moore homology of citeEM 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 citeEM and for ordinary affine Hecke algebras in citeMR3.
Classification : 18E30, 16E45, 16S37
Keywords: Koszul duality, Fourier transform, affine Hecke algebras 
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     author = {Mirkovi\'c, Ivan and Riche, Simon},
     title = {Linear {Koszul} duality and {Fourier} transform for convolution algebras},
     journal = {Documenta mathematica},
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     volume = {20},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a13/}
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Mirković, Ivan; Riche, Simon. Linear Koszul duality and Fourier transform for convolution algebras. Documenta mathematica, Tome 20 (2015), pp. 989-1038. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a13/