2014/01/28 by Ivan Mirkovic, Mirkovic, Ivan, Simon Riche +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1401.7186
v1: 29 pages; v2: 41 pages, many details added; v3: 42 pages, minor modifications (final version, to appear in Doc. Math.)
arxiv created 2015/09/14 · arxiv updated 2015/09/15
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).