Existence of Affine Pavings for Varieties of Partial Flags Associated to Nilpotent Elements
Existence of Affine Pavings for Varieties of Partial Flags Associated to Nilpotent Elements
复制标题
与幂零元相关的各种部分标志的仿射铺路的存在性
DOI：
10.1093/imrn/rnv134
复制
发表时间：
2013
影响因子：
1
通讯作者：
Lucas Fresse
中科院分区：
文献类型：
--
作者：
Lucas Fresse
根据定义，复数还原线性代数群 G 的标志变量是 Borel 子群的商 G/B。它可以被视为Lie(G)的Borel子代数集合。给定 Lie(G) 中的幂零元素 e，我们将 Springer 纤维称为由包含 e 的 Borel 子代数形成的子品种。施普林格纤维通常具有复杂的结构（不是不可约的、单一的）。然而，C. De Concini、G. Lusztig 和 C. Procesi 的定理断言，当 G 是经典的时，施普林格纤维总是可以由有限多个与仿射空间同构的子簇铺成。在本文中，我们研究将 Springer 纤维推广到部分旗形变体的变体，即抛物线子群（而不是 Borel 子群）的商 G/P 的子变体。本文的主要结果是 De Concini、Lusztig 和 Procesi 定理在此背景下的推广。
The flag variety of a complex reductive linear algebraic group G is by definition the quotient G/B by a Borel subgroup. It can be regarded as the set of Borel subalgebras of Lie(G). Given a nilpotent element e in Lie(G), one calls Springer fiber the subvariety formed by the Borel subalgebras which contain e. Springer fibers have in general a complicated structure (not irreducible, singular). Nevertheless, a theorem by C. De Concini, G. Lusztig, and C. Procesi asserts that, when G is classical, a Springer fiber can always be paved by finitely many subvarieties isomorphic to affine spaces. In this paper, we study varieties generalizing the Springer fibers to the context of partial flag varieties, that is, subvarieties of the quotient G/P by a parabolic subgroup (instead of a Borel subgroup). The main result of the paper is a generalization of De Concini, Lusztig, and Procesi's theorem to this context.