# Pfaffian sum formula for the symplectic Grassmannians

Takeshi Ikeda*, Tomoo Matsumura

*この研究の対応する著者

12 被引用数 (Scopus)

## 抄録

We study the torus equivariant Schubert classes of the Grassmannian of non-maximal isotropic subspaces in a symplectic vector space. We prove a formula that expresses each of those classes as a sum of multi Schur-Pfaffians, whose entries are equivariantly modified special Schubert classes. Our result gives a proof to Wilson’s conjectural formula, which generalizes the Giambelli formula for the ordinary cohomology proved by Buch–Kresch–Tamvakis, given in terms of Young’s raising operators. Furthermore we show that the formula extends to a certain family of Schubert classes of the symplectic partial isotropic flag varieties.

本文言語 English 269-306 38 Mathematische Zeitschrift 280 1-2 https://doi.org/10.1007/s00209-015-1423-x Published - 2015 6 1 はい

• 数学 (全般)

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