Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2015
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| _version_ | 1866914715603566592 |
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| author | Appel, Andrea Toledano-Laredo, Valerio |
| author_facet | Appel, Andrea Toledano-Laredo, Valerio |
| contents | Let g be a symmetrisable Kac-Moody algebra and V an integrable g-module in category O. We show that the monodromy of the (normally ordered) rational Casimir connection on V can be made equivariant with respect to the Weyl group W of g, and therefore defines an action of the braid group B_W of W on V. We then prove that this action is canonically equivalent to the quantum Weyl group action of B_W on a quantum deformation of V, that is an integrable, category O-module V_h over the quantum group U_h(g) such that V_h/hV_h is isomorphic to V. This extends a result of the second author which is valid for g semisimple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1512_03041 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra Appel, Andrea Toledano-Laredo, Valerio Quantum Algebra Algebraic Geometry Representation Theory Let g be a symmetrisable Kac-Moody algebra and V an integrable g-module in category O. We show that the monodromy of the (normally ordered) rational Casimir connection on V can be made equivariant with respect to the Weyl group W of g, and therefore defines an action of the braid group B_W of W on V. We then prove that this action is canonically equivalent to the quantum Weyl group action of B_W on a quantum deformation of V, that is an integrable, category O-module V_h over the quantum group U_h(g) such that V_h/hV_h is isomorphic to V. This extends a result of the second author which is valid for g semisimple. |
| title | Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra |
| topic | Quantum Algebra Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/1512.03041 |