| Autor: |
Yunpeng Xue |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 8, Iss 7, Pp 14997-15007 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2023765?viewType=HTML |
| Popis: |
Associated with a reductive algebraic group $ G $ and its rational representation $ (\rho, M) $ over an algebraically closed filed $ {\bf{k}} $, the authors define the enhanced reductive algebraic group $ {\underline{G}}: = G\ltimes_\rho M $, which is a product variety $ G\times M $ and endowed with an enhanced cross product in [5]. If $ {\underline{G}} = GL(V)\ltimes_{\eta} V $ with the natural representation $ (\eta, V) $ of $ {\text{GL}}(V) $, it is called an enhanced general linear algebraic group. And the authors give a precise classification of finite nilpotent orbits via a finite set of so-called enhanced partitions of $ n = \dim V $ for the enhanced group $ {\underline{G}} = {\text{GL}}(V)\ltimes_{\eta}V $ in [6, Theorem 3.5]. We will give another way to prove this classification theorem in this paper. Then we focus on the support variety of the Weyl module for $ {\underline{G}} = {\text{GL}}(V)\ltimes_{\eta}V $ in characteristic $ p $, and obtain that it coinsides with the closure of an enhanced nilpotent orbit under some mild condition. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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