On cacti and crystals
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866917689335742464 |
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| author | Berenstein, Arkady Greenstein, Jacob Li, Jian-Rong |
| author_facet | Berenstein, Arkady Greenstein, Jacob Li, Jian-Rong |
| contents | In the present work we study actions of various groups generated by involutions on the category $\mathscr O^{int}_q(\mathfrak g)$ of integrable highest weight $U_q(\mathfrak g)$-modules and their crystal bases for any symmetrizable Kac-Moody algebra $\mathfrak g$. The most notable of them are the cactus group and (yet conjectural) Weyl group action on any highest weight integrable module and its lower and upper crystal bases. Surprisingly, some generators of cactus groups are anti-involutions of the Gelfand-Kirillov model for $\mathscr O^{int}_q(\mathfrak g)$ closely related to the remarkable quantum twists discovered by Kimura and Oya. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_11330 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On cacti and crystals Berenstein, Arkady Greenstein, Jacob Li, Jian-Rong Quantum Algebra Representation Theory 17B37, 17B67 In the present work we study actions of various groups generated by involutions on the category $\mathscr O^{int}_q(\mathfrak g)$ of integrable highest weight $U_q(\mathfrak g)$-modules and their crystal bases for any symmetrizable Kac-Moody algebra $\mathfrak g$. The most notable of them are the cactus group and (yet conjectural) Weyl group action on any highest weight integrable module and its lower and upper crystal bases. Surprisingly, some generators of cactus groups are anti-involutions of the Gelfand-Kirillov model for $\mathscr O^{int}_q(\mathfrak g)$ closely related to the remarkable quantum twists discovered by Kimura and Oya. |
| title | On cacti and crystals |
| topic | Quantum Algebra Representation Theory 17B37, 17B67 |
| url | https://arxiv.org/abs/1803.11330 |