A geometric model for Hochschild homology of Soergel bimodules

Details A geometric model for Hochschild homology of Soergel bimodules A geometric model for Hochschild homology of Soergel bimodules

2007-07-13

arxiv.org/abs/0707.2003v2

Geometry and Topology 12 (2008), 1243--1263.

Mathematics

Algebraic Geometry

19 pages, no figures

Scientific paper

10.2140/gt.2008.12.1243

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.

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