Associated varieties of minimal highest weight modules
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2019
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913554484953088 |
|---|---|
| author | Bai, Zhanqiang Ma, Jia-Jun Xiao, Wei Xie, Xun |
| author_facet | Bai, Zhanqiang Ma, Jia-Jun Xiao, Wei Xie, Xun |
| contents | Let $\mathfrak{g}$ be a complex simple Lie algebra.
A simple $\mathfrak{g}$-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit.
The main result of this paper is a classification of minimal highest weight modules for $\\mathfrak{g}$. This classification extends the
work of Joseph, which focused on categorizing minimal highest weight modules annihilated by completely prime ideals.
Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_00914 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Associated varieties of minimal highest weight modules Bai, Zhanqiang Ma, Jia-Jun Xiao, Wei Xie, Xun Representation Theory Let $\mathfrak{g}$ be a complex simple Lie algebra. A simple $\mathfrak{g}$-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of this paper is a classification of minimal highest weight modules for $\\mathfrak{g}$. This classification extends the work of Joseph, which focused on categorizing minimal highest weight modules annihilated by completely prime ideals. Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties. |
| title | Associated varieties of minimal highest weight modules |
| topic | Representation Theory |
| url | https://arxiv.org/abs/1909.00914 |