تقرير
On the variety of 1-dimensional representations of finite $W$-algebras in low rank
| العنوان: | On the variety of 1-dimensional representations of finite $W$-algebras in low rank |
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| المؤلفون: | Brown, Jonathan, Goodwin, Simon M. |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Rings and Algebras |
| الوصف: | Let $\mathfrak g$ be a simple Lie algebra over $\mathbb C$ and let $e \in \mathfrak g$ be nilpotent. We consider the finite $W$-algebra $U(\mathfrak g,e)$ associated to $e$ and the problem of determining the variety $\mathcal E(\mathfrak g,e)$ of 1-dimensional representations of $U(\mathfrak g,e)$. For $\mathfrak g$ of low rank, we report on computer calculations that have been used to determine the structure of $\mathcal E(\mathfrak g,e)$, and the action of the component group $\Gamma_e$ of the centralizer of $e$ on $\mathcal E(\mathfrak g,e)$. As a consequence, we provide two examples where the nilpotent orbit of $e$ is induced, but there is a 1-dimensional $\Gamma_e$-stable $U(\mathfrak g,e)$-module which is not induced via Losev's parabolic induction functor. In turn this gives examples where there is a "non-induced" multiplicity free primitive ideal of $U(\mathfrak g)$. Comment: 13 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1708.08609 |
| رقم الأكسشن: | edsarx.1708.08609 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |