On the reducibility of scalar generalized Verma modules associated to two-step nilpotent parabolic subalgebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909363555270656 |
|---|---|
| author | Bai, Zhanqiang Fang, Minyan Wang, Zhaojun |
| author_facet | Bai, Zhanqiang Fang, Minyan Wang, Zhaojun |
| contents | Let $\mathfrak{g}$ be a simple complex Lie algebra.A generalized Verma module induced from a one-dimensional representation of a parabolic subalgebra of $\mathfrak{g}$ is called a scalar generalized Verma module of $\mathfrak{g}$. In this article, we use Gelfand-Kirillov dimension to determine the reducibility of scalar generalized Verma modules of $\mathfrak{g}$ associated to a two-step nilpotent parabolic subalgebra of non-maximal type. Such a module exists only when $\mathfrak{g}=\mathfrak{sl}(n,\mathbb{C})$, $\mathfrak{so}(2n,\mathbb{C})$ or $E_6$. We find that the reducible points of these modules can be drawn in a two-dimensional complex plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07415 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the reducibility of scalar generalized Verma modules associated to two-step nilpotent parabolic subalgebras Bai, Zhanqiang Fang, Minyan Wang, Zhaojun Representation Theory Let $\mathfrak{g}$ be a simple complex Lie algebra.A generalized Verma module induced from a one-dimensional representation of a parabolic subalgebra of $\mathfrak{g}$ is called a scalar generalized Verma module of $\mathfrak{g}$. In this article, we use Gelfand-Kirillov dimension to determine the reducibility of scalar generalized Verma modules of $\mathfrak{g}$ associated to a two-step nilpotent parabolic subalgebra of non-maximal type. Such a module exists only when $\mathfrak{g}=\mathfrak{sl}(n,\mathbb{C})$, $\mathfrak{so}(2n,\mathbb{C})$ or $E_6$. We find that the reducible points of these modules can be drawn in a two-dimensional complex plane. |
| title | On the reducibility of scalar generalized Verma modules associated to two-step nilpotent parabolic subalgebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2310.07415 |