تقرير
On induced completely prime primitive ideals in enveloping algebras of classical Lie algebras
| العنوان: | On induced completely prime primitive ideals in enveloping algebras of classical Lie algebras |
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| المؤلفون: | Goodwin, Simon M., Topley, Lewis, Westaway, Matthew |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Rings and Algebras, 17B35 (Primary), 16D60, 17B08, 17B10 (Secondary) |
| الوصف: | A distinguished family of completely prime primitive ideals in the universal enveloping algebra of a reductive Lie algebra ${\mathfrak g}$ over ${\mathbb C}$ are those ideals constructed from one-dimensional representations of finite $W$-algebras. We refer to these ideals as Losev--Premet ideals. For ${\mathfrak g}$ simple of classical type, we prove that for a Losev-Premet ideal $I$ in $U({\mathfrak g})$, there exists a Losev-Premet ideal $I_0$ for a certain Levi subalgebra ${\mathfrak g}_0$ of ${\mathfrak g}$ such that associated variety of $I_0$ is the closure of a rigid nilpotent orbit in ${\mathfrak g}_0$ and $I$ is obtained from $I_0$ by parabolic induction. This is deduced from the corresponding statement about one-dimensional representations of finite $W$-algebras. Comment: 24 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.10603 |
| رقم الأكسشن: | edsarx.2311.10603 |
| قاعدة البيانات: | arXiv |
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