A geometric model for Hochschild homology of Soergel bimodules
نویسندگان
چکیده
منابع مشابه
A Geometric Model for Hochschild Homology of Soergel Bimodules
An important step in the calculation of the triply graded link 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 × Borbit closures in G. We show that, in type A these orbit closures are equivariantly formal for ...
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The Soergel bimodules were introduced by Soergel in [9, 10] in the context of the infinite-dimensional representation theory of simple Lie algebra and Kazhdan-Lusztig theory. They have nice explicit expression as the tensor products of the rings of polynomials invariant under the action of a symmetric group, tensored over rings of the same form. Moreover, there are various quite different inter...
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We trade matrix factorizations and Koszul complexes for Hochschild homology of Soergel bimodules to modify the construction of triplygraded link homology and relate it to Kazhdan-Lusztig theory. Hochschild homology. Let R be a k-algebra, where k is a field, R = R ⊗k R op be the enveloping algebra of R, and M be an R-bimodule (equivalently, a left R-module). The functor of R-coinvariants associa...
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Lecture 11: Soergel Bimodules
In this lecture we continue to study the category O0 and explain some ideas towards the proof of the Kazhdan-Lusztig conjecture. We start by introducing projective functors Pi : O0 → O0 that act by w 7→ w(1 + si) on K0(O0). Using these functors we produce a projective generator of O0. In Section 2 we explain some of the work of Soergel that ultimately was used by Elias and Williamson to give a ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2008
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2008.12.1243