Standard Monomial Theory for Bott–Samelson Varieties
Standard Monomial Theory for Bott–Samelson Varieties
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DOI：
10.1023/a:1014396129323
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发表时间：
1997-03
影响因子：
1.8
通讯作者：
V. Lakshmibai;P. Littelmann;P. Magyar
中科院分区：
文献类型：
--
作者：
V. Lakshmibai;P. Littelmann;P. Magyar
Bott-Samelson簇是几何表示理论中的一个重要工具[1，3，10，25]。它们最初被定义为舒伯特变体的去奇异化，并具有舒伯特变体的许多特性。它们具有Borel子群的作用，并且Bott-Samelson簇的投射坐标环分裂成某些广义Demazure模（也出现在其他上下文中[22，23]）。由Seshadri和第一作者[15，16]发展，最近由第二作者[20]完成的标准单性理论，给出了与舒伯特簇相关的Demazure模的明确基础。本文推广了[20]中的技巧，给出了与Bott-Samelson簇相关的广义Demazure模的显式基，从而证明了第一和第三作者在[12]中所宣布结果的加强形式（另见[13]）.我们还得到了Kumar [10]和Mathieu [25]的上同调消失定理、Bott-Samelson簇的投射正规性和Demazure特征公式的更初等的证明。
Bott–Samelson varieties are an important tool in geometric representation theory [1, 3, 10, 25]. They were originally defined as desingularizations of Schubert varieties and share many of the properties of Schubert varieties. They have an action of a Borel subgroup, and the projective coordinate ring of a Bott–Samelson variety splits into certain generalized Demazure modules (which also appear in other contexts [22, 23]). Standard Monomial Theory, developed by Seshadri and the first author [15, 16], and recently completed by the second author [20], gives explicit bases for the Demazure modules associated to Schubert varieties. In this paper, we extend the techniques of [20] to give explicit bases for the generalized Demazure modules associated to Bott–Samelson varieties, thus proving a strengthened form of the results announced by the first and third authors in [12] (see also [13]). We also obtain more elementary proofs of the cohomology vanishing theorems of Kumar [10] and Mathieu [25]; of the projective normality of Bott–Samelson varieties; and of the Demazure character formula.