A tableau formula for vexillary Schubert polynomials in type C

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-...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Author: Matsumura, Tomoo
Format: Article
Language:English
Subjects:
Combinatorial analysis
Homology
Mathematical analysis
Permutations
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422