Geodesic
A tableau formula for vexillary Schubert polynomials in type \(C\)
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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Ikeda-Mihalcea-Naruse's double Schubert polynomials [Adv. Math. 226 (2011)] 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 functions in terms of 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 corresponds to flagged marked shifted tableaux.
DOI : 10.37236/11091
Classification : 05E05, 05E10, 14M15
Mots-clés : Schubert polynomials, tableaux, partitions, Schur-Pfaffians 
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     author = {Tomoo Matsumura},
     title = {A tableau formula for vexillary {Schubert} polynomials in type {\(C\)}},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {1},
     doi = {10.37236/11091},
     zbl = {1512.05394},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11091/}
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Tomoo Matsumura. A tableau formula for vexillary Schubert polynomials in type \(C\). The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11091

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