منابع مشابه
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 ...
متن کاملHochschild homology of certain Soergel bimodules
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...
متن کاملSoergel Bimodules and the Shape of Bruhat Intervals
Given an element w of a Coxeter group, let ai(w) be the number of elements less than w in Bruhat order. A theorem of Björner and Ekedahl states that if W is crystallographic, then ai(w) ≤ aj(w) for all 0 ≤ i < j ≤ `(w) − i. Their proof uses the hard Lefschetz property in intersection cohomology. In this note we extend Björner and Ekedahl’s theorem to all Coxeter groups using the hard Lefschetz ...
متن کاملSimple Transitive 2-Representations of Soergel Bimodules in Type B2
We prove that every simple transitive 2-representation of the fiat 2-category of Soergel bimodules (over the coinvariant algebra) in type B2 is equivalent to a cell 2-representation. We also describe some general properties of the 2-category of Soergel bimodules for arbitrary finite Dihedral groups.
متن کاملTriply-graded link homology and Hochschild homology of Soergel bimodules
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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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2014
ISSN: 0003-486X
DOI: 10.4007/annals.2014.180.3.6