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2008 A geometric model for Hochschild homology of Soergel bimodules
Ben Webster, Geordie Williamson
Geom. Topol. 12(2): 1243-1263 (2008). DOI: 10.2140/gt.2008.12.1243

Abstract

An important step in the calculation of the triply graded link homology 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 B–equivariant intersection cohomology of B×B–orbit closures in G. We show that, in type A, these orbit closures are equivariantly formal for the conjugation B–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 to describe its Hilbert series, proving a conjecture of Jacob Rasmussen.

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Ben Webster. Geordie Williamson. "A geometric model for Hochschild homology of Soergel bimodules." Geom. Topol. 12 (2) 1243 - 1263, 2008. https://doi.org/10.2140/gt.2008.12.1243

Information

Received: 8 August 2007; Revised: 19 December 2007; Accepted: 15 March 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1198.20037
MathSciNet: MR2425548
Digital Object Identifier: 10.2140/gt.2008.12.1243

Subjects:
Primary: 17B10
Secondary: 57T10

Rights: Copyright © 2008 Mathematical Sciences Publishers

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