%0 Journal Article
%T A geometric model for Hochschild homology of Soergel bimodules
%A Ben Webster
%A Geordie Williamson
%J Mathematics
%D 2007
%I arXiv
%R 10.2140/gt.2008.12.1243
%X An important step in the calculation of the triply graded link homology theory of Khovanov and Rozansky is the determination of the Hochschild homology of Soergel bimodules for SL(n). We present a geometric model for this Hochschild homology for any simple group G, as equivariant intersection homology of B x B-orbit closures in G. We show that, in type A these orbit closures are equivariantly formal for the conjugation T-action. We use this fact to show that in the case where the corresponding orbit closure is smooth, this Hochschild homology is an exterior algebra over a polynomial ring on generators whose degree is explicitly determined by the geometry of the orbit closure, and describe its Hilbert series, proving a conjecture of Jacob Rasmussen.
%U http://arxiv.org/abs/0707.2003v2