Linear Koszul duality and Fourier transform for convolution algebrasReport as inadecuate




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* Corresponding author 1 UMass Amherst - University of Massachusetts Amherst 2 INSMI CNRS 3 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.





Author: Ivan Mirkovic - Simon Riche -

Source: https://hal.archives-ouvertes.fr/



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