Singular Soergel bimodules

By Geordie Williamson. 2010

93 citations recorded by the source corpus.

We define and study categories of singular Soergel bimodules, which are certain natural generalisations of Soergel bimodules. Indecomposable singular Soergel bimodules are classified, and we conclude that the split Grothendieck group of the 2-category of singular Soergel bimodules is isomorphic to the Schur algebroid. Soergel's conjecture on the characters of indecomposable Soergel bimodules in characteristic zero is shown to imply a similar conjecture for the characters of singular Soergel bimodules.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d87fe6c995666138a8eac0150c5122485adff5b4

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In Algebra and Number Theory

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Citations in the corpus

A diagrammatic categorification of the q-Schur algebra (2010, methodology): “Webster and Williamson subsequently showed our conjecture to be true, using a generalization of their geometric approach [38].”
Light ladders and clasp conjectures (2015, background): “The geometric Satake equivalence, or a (q-deformed) algebraic version developed in [5], will take a tensor product of fundamental representations and return a singular Soergel bimodule associated to the affine Weyl group, as in [29].”
Super $q$-Howe duality and web categories (2015, unknown): “ch also leads to diagrammatic presentations for categories gl NjM-Mod es of U q(gl NjM)-modules tensor generated 2Adding only column idempotents, one obtains the type A Schur algebroids introduced in [30]. 3We use colored diagrams in this paper. The colors (black, green and red) are important and we”
Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “To each functor Θ+i κ+i Θ +i κ respectively Θ −iκ κ−i Θ −i κ we associate a singular Soergel bimodule in the sense of [79], [86] that is a certain (R+i,R) respectively (R−i,R)-bimodule, as follows.”
The two-color Soergel calculus (2013, methodology): “for every reduced expression w. Then F is an equivalence. Proof. Left to the reader. 2.4. The Hecke Algebroid. 2.4.1. Deﬁnitions. The Hecke algebroid is a general construction for Coxeter groups. See [42] for more details. It will be useful to distinguish between the index s∈ Sand the parabolic subs”