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arXiv · 1401.3073

Pfaffian sum formula for the symplectic Grassmannians

Takeshi Ikeda·Tomoo Matsumura
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Abstract

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.

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Takeshi Ikeda, Tomoo Matsumura. 2014-01-14. Pfaffian sum formula for the symplectic Grassmannians. https://arxiv.org/abs/1401.3073

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