Representations of quantum groups arising from the Stokes phenomenon
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913317333762048 |
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| author | Xu, Xiaomeng |
| author_facet | Xu, Xiaomeng |
| contents | In this paper we prove that the quantum Stokes matrices of the quantum differential equation at a second order pole give rise to representations of the quantum group $U_q(\frak{gl}_n)$. We explain our results from the viewpoint of deformation quantization of the classical Stokes matrices at a second order pole. As a consequence, we can get a dictionary between the theory of Stokes phenomenon and the theory of quantum groups. We briefly discuss several such correspondences, and outline the generalization of our results to all classical types of Lie algebras and to the quantum differential equation at an arbitrary order pole. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_15673 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Representations of quantum groups arising from the Stokes phenomenon Xu, Xiaomeng Representation Theory Classical Analysis and ODEs Quantum Algebra In this paper we prove that the quantum Stokes matrices of the quantum differential equation at a second order pole give rise to representations of the quantum group $U_q(\frak{gl}_n)$. We explain our results from the viewpoint of deformation quantization of the classical Stokes matrices at a second order pole. As a consequence, we can get a dictionary between the theory of Stokes phenomenon and the theory of quantum groups. We briefly discuss several such correspondences, and outline the generalization of our results to all classical types of Lie algebras and to the quantum differential equation at an arbitrary order pole. |
| title | Representations of quantum groups arising from the Stokes phenomenon |
| topic | Representation Theory Classical Analysis and ODEs Quantum Algebra |
| url | https://arxiv.org/abs/2012.15673 |