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

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arxiv 1210.2066 v1 pith:TTYJATWO submitted 2012-10-07 math.AG math.CO

David Anderson , William Fulton This is my paper · ORCID
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keywords locitypescorrespondingdegeneracyformulaspfaffianssignedvexillary
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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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Cited by 2 Pith papers

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  1. Tableau formula for vexillary double Edelman--Greene coefficients

    math.CO 2024-12 conditional novelty 7.0 of 10

    For vexillary permutations, the double beta-Edelman-Greene coefficients are shown to be sums of Graham-positive monomials indexed by semistandard set-valued tableaux, with new restrictions on the types of factors appearing.

  2. Characteristic classes of symmetric and skew-symmetric degeneracy loci

    math.AG 2019-08 conditional novelty 6.0 of 10

    Explicit formulas for Chern-Schwartz-MacPherson classes of all GL_n(C)-orbits in symmetric and skew-symmetric matrices, via a sieve method and an interpolation method.

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