Degeneracy Loci, Pfaffians, and Vexillary Signed Permutations in Types B, C, and D
Degeneracy Loci, Pfaffians, and Vexillary Signed Permutations in Types B, C, and D
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B、C 和 D 型中的简并位点、Pfaffians 和 Vexillary 有符号排列
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
W. Fulton
中科院分区：
文献类型：
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作者：
David Anderson;W. Fulton
定义了B、C和D型向量丛的vexillary符号置换的概念，对应于具有这些类型对称性的向量丛的自然退化轨迹。我们表明，这些轨迹的类给出明确的Pfweian公式。Kazarian的Grassmannian公式是重要的特例，而池田、Mihalcea和Naruse的相应的双Schubert多项式被证明等于这些Pfuberans。
We define a notion of vexillary signed permutation in types B, C, and D, corresponding to natural degeneracy loci for vector bundles with symmetries of those types. We show that the classes of these loci are given by explicit Pfaffian formulas. The Grassmannian formulas of Kazarian are important special cases, and the corresponding double Schubert polynomials of Ikeda, Mihalcea, and Naruse are shown to be equal to these Pfaffians.