Paving Hessenberg varieties by affines
Paving Hessenberg varieties by affines
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通过仿射铺平 Hessenberg 品种
DOI：
10.1007/s00029-007-0038-4
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Julianna Tymoczko
中科院分区：
文献类型：
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作者：
Julianna Tymoczko
摘要：正则幂零Hessenberg簇形成了旗簇的一系列子簇，这些子簇在量子上同调、几何表示理论和数值分析的研究中出现。本文构造了正则幂零Hessenberg簇的仿射铺路，推广了De Concini-Lusztig-Procesi和Kostant的结果.这个铺路实际上是一个特定的Bruhat分解与Hessenberg多样性的交集。铺路的非空细胞和它们的尺寸确定的组合条件根。我们利用铺路证明了这些Hessenberg簇没有奇维同调。
Abstract.Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent Hessenberg varieties for all classical types, generalizing results of De Concini–Lusztig–Procesi and Kostant. This paving is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties have no odd-dimensional homology.