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arXiv · 1908.11531

A tableau formula for vexillary Schubert polynomials in type C

Tomoo Matsumura
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Abstract

Ikeda-Mihalcea-Naruse's double Schubert polynomials represent the equivariant cohomology classes of Schubert varieties in the type C flag varieties. The goal of this paper is to obtain a new tableau formula of these polynomials associated to vexillary signed permutations introduced by Anderson-Fulton. To achieve that goal, we introduce flagged factorial (Schur) $Q$-functions, combinatorially defined in terms of (flagged) marked shifted tableaux for flagged strict partitions, and prove their Schur-Pfaffian formula. As an application, we also obtain a new combinatorial formula of factorial $Q$-functions of Ivanov in which monomials bijectively correspond to flagged marked shifted tableaux.

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Tomoo Matsumura. 2019-08-30. A tableau formula for vexillary Schubert polynomials in type C. https://arxiv.org/abs/1908.11531

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