Singular Soergel bimodules
Representation Theory
2024-01-03 v3 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.1010.1283,
title = {Singular Soergel bimodules},
author = {Geordie Williamson},
journal= {arXiv preprint arXiv:1010.1283},
year = {2024}
}
Comments
v3: appended erratum addressing issue pointed out by Abe, Brundan, Elias and Patimo