Singular Soergel bimodules

Details Singular Soergel bimodules Singular Soergel bimodules

2010-10-06

arxiv.org/abs/1010.1283v2

Mathematics

Representation Theory

52 pages; two minor changes; Int Math Res Notices (2010)

Scientific paper

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.

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