A tableau formula for vexillary Schubert polynomials in type C

TL;DR

This paper introduces a new tableau formula for vexillary Schubert polynomials in type C, using flagged factorial Q-functions and combinatorial tableaux, advancing the understanding of equivariant cohomology in algebraic geometry.

Contribution

It develops a novel tableau formula for vexillary Schubert polynomials in type C using flagged factorial Q-functions and combinatorial tableaux, linking algebraic and combinatorial approaches.

Findings

Derived a Schur-Pfaffian formula for flagged factorial Q-functions.

Provided a new combinatorial formula for Ivanov's factorial Q-functions.

Established a bijective correspondence between monomials and flagged marked shifted tableaux.

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.