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arXiv · 1210.2066

Degeneracy Loci, Pfaffians, and Vexillary Signed Permutations in Types B, C, and D

David Anderson·William Fulton
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Abstract

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.

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David Anderson, William Fulton. 2012-10-07. Degeneracy Loci, Pfaffians, and Vexillary Signed Permutations in Types B, C, and D. https://arxiv.org/abs/1210.2066

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