Pure braid group actions on category O modules
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913187924803584 |
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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 U_h(g) its quantised enveloping algebra. Answering a question of P. Etingof, we prove that the quantum Weyl group operators of U_h(g) give rise to a canonical action of the pure braid group of g on any category O (not necessarily integrable) U_h(g)-module V. By relying on our recent results in arXiv:1512.03041, we show that this action describes the monodromy of the rational Casimir connection on the g-module corresponding to V under the Etingof-Kazhdan equivalence of category O for g and U_h(g). We also extend these results to yield equivalent quantum Weyl group and monodromic representations of parabolic pure braid groups on parabolic category O for U_h(g) and g. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05331 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pure braid group actions on category O modules Appel, Andrea Toledano-Laredo, Valerio Quantum Algebra Algebraic Geometry Representation Theory Let g be a symmetrisable Kac-Moody algebra and U_h(g) its quantised enveloping algebra. Answering a question of P. Etingof, we prove that the quantum Weyl group operators of U_h(g) give rise to a canonical action of the pure braid group of g on any category O (not necessarily integrable) U_h(g)-module V. By relying on our recent results in arXiv:1512.03041, we show that this action describes the monodromy of the rational Casimir connection on the g-module corresponding to V under the Etingof-Kazhdan equivalence of category O for g and U_h(g). We also extend these results to yield equivalent quantum Weyl group and monodromic representations of parabolic pure braid groups on parabolic category O for U_h(g) and g. |
| title | Pure braid group actions on category O modules |
| topic | Quantum Algebra Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2208.05331 |