Singular Soergel bimodules

Geordie Williamson

Singular Soergel bimodules

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1010.1283 v3 pith:G2WDRIWM submitted 2010-10-06 math.RT math.QA

Geordie Williamson This is my paper · ORCID

classification math.RTmath.QA

keywords soergelbimodulessingularcharactersconjectureindecomposablealgebroidcategories

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Idempotents, traces, and dimensions in Hecke categories
math.RT 2025-07 conditional novelty 8.0 of 10

The paper provides closed formulas for recursible local intersection forms and recursive partial trace formulas that reduce categorical dimensions in asymptotic Hecke categories to diagrammatic computations.

Pith tools