On the annihilator variety of a highest weight Harish-Chandra module
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910566369460224 |
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| author | Bai, Zhanqiang Jiang, Jing |
| author_facet | Bai, Zhanqiang Jiang, Jing |
| contents | Let $G$ be a Hermitian type Lie group with maximal compact subgroup $K$. Let $L(λ)$ be a highest weight Harish-Chandra module of $G$ with the infinitesimal character $λ$. By using some combinatorial algorithm, we obtain a description of the annihilator variety of $L(λ)$. As an application, when $L(λ)$ is unitarizable, we prove that the Gelfand-Kirillov dimension of $L(λ)$ only depends on the value of $z=(λ,β^{\vee})$, where $β$ is the highest root. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07951 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the annihilator variety of a highest weight Harish-Chandra module Bai, Zhanqiang Jiang, Jing Representation Theory Rings and Algebras Let $G$ be a Hermitian type Lie group with maximal compact subgroup $K$. Let $L(λ)$ be a highest weight Harish-Chandra module of $G$ with the infinitesimal character $λ$. By using some combinatorial algorithm, we obtain a description of the annihilator variety of $L(λ)$. As an application, when $L(λ)$ is unitarizable, we prove that the Gelfand-Kirillov dimension of $L(λ)$ only depends on the value of $z=(λ,β^{\vee})$, where $β$ is the highest root. |
| title | On the annihilator variety of a highest weight Harish-Chandra module |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2408.07951 |