Representations of shifted affine quantum groups and Coulomb branches
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915697326555136 |
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| author | Varagnolo, Michela Vasserot, Eric |
| author_facet | Varagnolo, Michela Vasserot, Eric |
| contents | We compare the integral category O of shifted affine quantum groups of symmetric and non symmetric types. To do so we compute the K-theoretic analog of the Coulomb branches with symmetrizers introduced by Nakajima and Weekes. This yields an equivalence of the category O with a module category over a new type of quiver Hecke algebras. At the decategorified level, this establishes a connection between the Grothendieck group of O and a finite-dimensional module over a simple Lie algebra of unfolded symmetric type. We compute this module in certain cases and give a combinatorial rule for its crystal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Representations of shifted affine quantum groups and Coulomb branches Varagnolo, Michela Vasserot, Eric Representation Theory We compare the integral category O of shifted affine quantum groups of symmetric and non symmetric types. To do so we compute the K-theoretic analog of the Coulomb branches with symmetrizers introduced by Nakajima and Weekes. This yields an equivalence of the category O with a module category over a new type of quiver Hecke algebras. At the decategorified level, this establishes a connection between the Grothendieck group of O and a finite-dimensional module over a simple Lie algebra of unfolded symmetric type. We compute this module in certain cases and give a combinatorial rule for its crystal. |
| title | Representations of shifted affine quantum groups and Coulomb branches |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2503.06262 |