Category O for quantum loop algebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911156891811840 |
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| author | Neguţ, Andrei |
| author_facet | Neguţ, Andrei |
| contents | We generalize the Hernandez-Jimbo category O of representations of Borel subalgebras of quantum affine algebras to the case of quantum loop algebras for arbitrary Kac-Moody g (as well as related algebras, such as quantum toroidal gl_1). Moreover, we give explicit realizations of all simple modules, and devise tools for the computation of q-characters that are new even for g of finite type. Our techniques allow us to generalize classic results of Frenkel-Hernandez, Frenkel-Mukhin, Hernandez-Jimbo and Hernandez-Leclerc, as well as prove conjectures of Feigin-Jimbo-Miwa-Mukhin and Mukhin-Young. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Category O for quantum loop algebras Neguţ, Andrei Representation Theory Quantum Algebra We generalize the Hernandez-Jimbo category O of representations of Borel subalgebras of quantum affine algebras to the case of quantum loop algebras for arbitrary Kac-Moody g (as well as related algebras, such as quantum toroidal gl_1). Moreover, we give explicit realizations of all simple modules, and devise tools for the computation of q-characters that are new even for g of finite type. Our techniques allow us to generalize classic results of Frenkel-Hernandez, Frenkel-Mukhin, Hernandez-Jimbo and Hernandez-Leclerc, as well as prove conjectures of Feigin-Jimbo-Miwa-Mukhin and Mukhin-Young. |
| title | Category O for quantum loop algebras |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2501.00724 |