On the associated variety of a highest weight Harish-Chandra module
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866914678696837120 |
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| author | Bai, Zhanqiang Hunziker, Markus Xie, Xun Zierau, Roger |
| author_facet | Bai, Zhanqiang Hunziker, Markus Xie, Xun Zierau, Roger |
| contents | We prove a simple formula that calculates the associated variety of a highest weight Harish-Chandra module directly from its highest weight. We also give a formula for the Gelfand--Kirillov dimension of highest weight Harish-Chandra module which is uniform across Cartan types and is valid for arbitrary infinitesimal character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08886 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the associated variety of a highest weight Harish-Chandra module Bai, Zhanqiang Hunziker, Markus Xie, Xun Zierau, Roger Representation Theory 22E47 (Primary) 17B10 (Secondary) We prove a simple formula that calculates the associated variety of a highest weight Harish-Chandra module directly from its highest weight. We also give a formula for the Gelfand--Kirillov dimension of highest weight Harish-Chandra module which is uniform across Cartan types and is valid for arbitrary infinitesimal character. |
| title | On the associated variety of a highest weight Harish-Chandra module |
| topic | Representation Theory 22E47 (Primary) 17B10 (Secondary) |
| url | https://arxiv.org/abs/2402.08886 |