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    Mathematics, Northeastern University, Boston

    A geometric model for Hochschild homology of Soergel bimodules

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    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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    Description

    Title : A geometric model for Hochschild homology of Soergel bimodules
    Author(s) : Ben Webster, Geordie Williamson
    Abstract : 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.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 2007

    Affiliations Mathematics, Northeastern University, Boston
    Journal : Geometry and Topology
    Volume : 12
    Issue : 2
    Pages : 1243 - 1263
    Url : http://www.msp.warwick.ac.uk/gt/2008/12-02/p027.xhtml
    Doi : 10.2140/gt.2008.12.1243

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