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- W2663527558 abstract "The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the closures of these orbits have polynomial representatives $hat{mathfrak{S}}^{tt{FPF}}_z$ akin to Schubert polynomials. We show that the fixed-point-free involution Stanley symmetric functions $hat{F}^{tt{FPF}}_z$, which are stable limits of the polynomials $hat{mathfrak{S}}^{tt{FPF}}_z$, are Schur $P$-positive. To do so, we construct an analogue of the Lascoux-Schutzenberger tree, an algebraic recurrence that computes Schubert polynomials. As a byproduct of our proof, we obtain a Pfaffian formula of geometric interest for $hat{mathfrak{S}}^{tt{FPF}}_z$ when $z$ is a fixed-point-free version of a Grassmannian permutation. We also classify the fixed-point-free involution Stanley symmetric functions that are single Schur $P$-functions, and show that the decomposition of $hat{F}^{tt{FPF}}_z$ into Schur $P$-functions is unitriangular with respect to dominance order on strict partitions. These results and proofs mirror previous work by the authors related to the orthogonal group action on the type A flag variety." @default.
- W2663527558 created "2017-06-30" @default.
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- W2663527558 date "2020-01-01" @default.
- W2663527558 modified "2023-10-18" @default.
- W2663527558 title "Fixed-point-free involutions and Schur $P$-positivity" @default.
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- W2663527558 doi "https://doi.org/10.4310/joc.2020.v11.n1.a4" @default.
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