Quantum Sugawara operators in type $A$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917762923757568 |
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| author | Jing, Naihuan Liu, Ming Molev, Alexander |
| author_facet | Jing, Naihuan Liu, Ming Molev, Alexander |
| contents | We construct Sugawara operators for the quantum affine algebra of type $A$ in an explicit form. The operators are associated with primitive idempotents of the Hecke algebra and parameterized by Young diagrams. This generalizes a previous construction (2016) where one-column diagrams were considered. We calculate the Harish-Chandra images of the Sugawara operators and identify them with the eigenvalues of the operators acting in the $q$-deformed Wakimoto modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11435 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum Sugawara operators in type $A$ Jing, Naihuan Liu, Ming Molev, Alexander Quantum Algebra Mathematical Physics Representation Theory We construct Sugawara operators for the quantum affine algebra of type $A$ in an explicit form. The operators are associated with primitive idempotents of the Hecke algebra and parameterized by Young diagrams. This generalizes a previous construction (2016) where one-column diagrams were considered. We calculate the Harish-Chandra images of the Sugawara operators and identify them with the eigenvalues of the operators acting in the $q$-deformed Wakimoto modules. |
| title | Quantum Sugawara operators in type $A$ |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2212.11435 |