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arXiv 1908.013372019-08math.AGmath.RT

高度为2的幂零轨道与仿射Weyl群中的对合

Nilpotent orbits of height 2 and involutions in the affine Weyl group

Jacopo Gandini, Pierluigi Moseneder Frajria, Paolo Papi

备注：: v2: 28 pages, 1 table. Minor revision. To appear in Indag. Math
发表信息：: Indag. Math. (N.S.) 31 (2020), no. 4, 568-594

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AI总结：

本文研究特征零域上几乎单群的Borel子群在高度至多为2的幂零元素簇上的有限轨道作用，用两两正交根集合参数化B-轨道，并用仿射Weyl群中对合的Bruhat序完整刻画轨道闭包间的包含关系。

摘要：

设G是特征为零的代数闭域k上的一个几乎单群，设g是其李代数，并设B是G的一个Borel子群。则B在g中高度至多为2的幂零元素所构成的簇N_2上以有限多个轨道的方式作用。我们利用两两正交根的集合给出了N_2中B-轨道的一个参数化，并借助g的仿射Weyl群中某些对合上的Bruhat序，给出了B-轨道闭包之间包含关系的完整描述。

英文摘要：

Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in g whose height is at most 2. We provide a parametrization of the B-orbits in N_2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g.

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