Report
Parabolic induction for Springer fibres
| العنوان: | Parabolic induction for Springer fibres |
|---|---|
| المؤلفون: | Topley, Lewis, Saunders, Neil |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Combinatorics |
| الوصف: | Let $G$ be a reductive group satisfying the standard hypotheses, with Lie algebra $\mathfrak{g}$. For each nilpotent orbit $\mathcal{O}_0$ in a Levi subalgebra $\mathfrak{g}_0$ we can consider the induced orbit $\mathcal{O}$ defined by Lusztig and Spaltenstein. We observe that there is a natural closed morphism of relative dimension zero from the Springer fibre over a point of $\mathcal{O}_0$ to the Springer fibre over $\mathcal{O}$, which induces an injection on the level of irreducible components. When $G = \operatorname{GL}_N$ the components of Springer fibres was classified by Spaltenstein using standard tableaux. Our main results explains how the Lusztig--Spaltenstein map of Springer fibres can be described combinatorially, using a new associative composition rule for standard tableaux which we call stacking. Comment: 15 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2112.09923 |
| رقم الانضمام: | edsarx.2112.09923 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |