Cyclotomic nil-Brauer and Singular Soergel bimodules of type D
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| Format: | Preprint |
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2024
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| _version_ | 1866917099029397504 |
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| author | Bodish, Elijah Brundan, Jonathan Elias, Ben |
| author_facet | Bodish, Elijah Brundan, Jonathan Elias, Ben |
| contents | We introduce a new family of monoidal categories which are cyclotomic quotients of the nil-Brauer category. We construct a monoidal functor from the cyclotomic nil-Brauer category to another monoidal category constructed from singular Soergel bimodules of type D. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclotomic nil-Brauer and Singular Soergel bimodules of type D Bodish, Elijah Brundan, Jonathan Elias, Ben Representation Theory 17B37, 18N25, 16D20 We introduce a new family of monoidal categories which are cyclotomic quotients of the nil-Brauer category. We construct a monoidal functor from the cyclotomic nil-Brauer category to another monoidal category constructed from singular Soergel bimodules of type D. 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. |
| title | Cyclotomic nil-Brauer and Singular Soergel bimodules of type D |
| topic | Representation Theory 17B37, 18N25, 16D20 |
| url | https://arxiv.org/abs/2410.15167 |