Tensor ideals of abelian type and quantum groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918225163321344 |
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| author | Coulembier, Kevin Etingof, Pavel Ostrik, Victor |
| author_facet | Coulembier, Kevin Etingof, Pavel Ostrik, Victor |
| contents | We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum groups as well as to some representation categories of finite groups. In an appendix on Duflo involutions in monoidal categories, we make a connection between Duflo involutions in the affine Weyl group and tensor ideals for quantum groups, and prove some of Lusztig's conjectures for arbitrary Coxeter groups, at equal parameters, without invoking the boundedness hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor ideals of abelian type and quantum groups Coulembier, Kevin Etingof, Pavel Ostrik, Victor Quantum Algebra Representation Theory We initiate a study of tensor ideals in linear rigid monoidal categories that are kernels of linear monoidal functors to abelian monoidal categories. We develop general methods and apply them to the category of tilting modules over quantum groups as well as to some representation categories of finite groups. In an appendix on Duflo involutions in monoidal categories, we make a connection between Duflo involutions in the affine Weyl group and tensor ideals for quantum groups, and prove some of Lusztig's conjectures for arbitrary Coxeter groups, at equal parameters, without invoking the boundedness hypothesis. |
| title | Tensor ideals of abelian type and quantum groups |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2511.08859 |