تقرير
Monogamous subvarieties of the nilpotent cone
| العنوان: | Monogamous subvarieties of the nilpotent cone |
|---|---|
| المؤلفون: | Goodwin, Simon M., Pengelly, Rachel, Stewart, David I., Thomas, Adam R. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, 17B45 (Primary) 17B50 (Secondary) |
| الوصف: | Let $G$ be a reductive algebraic group over an algebraically closed field $k$ of prime characteristic not $2$, whose Lie algebra is denoted $\mathfrak{g}$. We call a subvariety $\mathfrak{X}$ of the nilpotent cone $N \subset \mathfrak{g}$ monogamous if for every $e\in \mathfrak{X}$, the $\mathfrak{sl}_2$-triples $(e,h,f)$ with $f\in \mathfrak{X}$ are conjugate under the centraliser $C_G(e)$. Building on work by the first two authors, we show there is a unique maximal closed $G$-stable monogamous subvariety $V \subset N$ and that it is an orbit closure, hence irreducible. We show that $V$ can also be characterised in terms of Serre's $G$-complete reducibility. Comment: 15 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.20025 |
| رقم الأكسشن: | edsarx.2406.20025 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |