摘要翻译:
经典的Ehresmann-Bruhat序描述了有限维向量空间V中一对标志的可能退化;或者,等价地,作用于两个全旗变体的直积的群GL(V)的轨道的闭包。对于V中由两个子空间和一个部分标志组成的三元组,我们得到了类似的结果;这相当于描述两个Grassmannian和一个标志变种乘积中的一个GL(V)轨道的闭包。我们给出了一个秩准则来检验这样一个三元组是否可以退化为另一个三元组,并对最小退化进行了分类。我们的方法只涉及初等线性代数和图的组合学(起源于Auslander-Reiten颤动)。
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英文标题:
《Bruhat order for two subspaces and a flag》
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作者:
Evgeny Smirnov
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Representation Theory 表象理论
分类描述:Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示,李理论,结合代数,多重线性代数
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Combinatorics 组合学
分类描述:Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学,图论,计数,组合优化,拉姆齐理论,组合对策论
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英文摘要:
The classical Ehresmann-Bruhat order describes the possible degenerations of a pair of flags in a finite-dimensional vector space V; or, equivalently, the closure of an orbit of the group GL(V) acting on the direct product of two full flag varieties. We obtain a similar result for triples consisting of two subspaces and a partial flag in V; this is equivalent to describing the closure of a GL(V)-orbit in the product of two Grassmannians and one flag variety. We give a rank criterion to check whether such a triple can be degenerated to another one, and we classify the minimal degenerations. Our methods involve only elementary linear algebra and combinatorics of graphs (originating in Auslander-Reiten quivers).
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PDF链接:
https://arxiv.org/pdf/0704.3061