Cyclotomic nil-Brauer and singular Soergel bimodules of type D
Abstract
We study a new family of strict monoidal categories, which are cyclotomic quotients of the nil-Brauer category. We construct a monoidal functor from the cyclotomic nil-Brauer category of level l l to another monoidal category constructed from singular Soergel bimodules of type A l − 1 ∖ D l / A l − 1 \operatorname {A}_{l-1} \backslash \operatorname {D}_l / \operatorname {A}_{l-1} . We conjecture that our functor is an equivalence of categories. Although we can prove neither fullness nor faithfulness at this point, we are able to show that the functor induces an isomorphism at the level of Grothendieck rings. We compute these rings and their canonical bases, and give diagrammatic descriptions of the corresponding primitive idempotents.
Fields of Study & Subjects
Advanced Topics in Algebra
Cyclopropane Reaction Mechanisms
Asymmetric Hydrogenation and Catalysis
Publication details
- Journal / source
- Representation Theory of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 30
- Issue
- 3
- Pages
- 68–133
- Publication date
- 15 April 2026
- Language
- EN