Irreducible modules of modular Lie superalgebras and super version of the first Kac-Weisfeiler conjecture
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929533916020736 |
|---|---|
| author | Shu, Bin |
| author_facet | Shu, Bin |
| contents | Suppose $g=g_0+g_1$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the universal enveloping algebra $U(g)$ of $g$, as a super generalization of the celebrated first Kac-Weisfeiler conjecture. It is demonstrated that the conjecture holds for all basic classical Lie superalgebras and all completely solvable restricted Lie superalgebras. In this process, we investigate irreducible representations of solvable Lie superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08666 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Irreducible modules of modular Lie superalgebras and super version of the first Kac-Weisfeiler conjecture Shu, Bin Representation Theory 17B50, 17B20, 17B30 Suppose $g=g_0+g_1$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the universal enveloping algebra $U(g)$ of $g$, as a super generalization of the celebrated first Kac-Weisfeiler conjecture. It is demonstrated that the conjecture holds for all basic classical Lie superalgebras and all completely solvable restricted Lie superalgebras. In this process, we investigate irreducible representations of solvable Lie superalgebras. |
| title | Irreducible modules of modular Lie superalgebras and super version of the first Kac-Weisfeiler conjecture |
| topic | Representation Theory 17B50, 17B20, 17B30 |
| url | https://arxiv.org/abs/2312.08666 |