Pfaffian sum formula for the symplectic Grassmannians
Algebraic Geometry
2015-06-18 v3 Combinatorics
Representation Theory
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.
Cite
@article{arxiv.1401.3073,
title = {Pfaffian sum formula for the symplectic Grassmannians},
author = {Takeshi Ikeda and Tomoo Matsumura},
journal= {arXiv preprint arXiv:1401.3073},
year = {2015}
}
Comments
Version 3: an error of a proof in the previous version has been fixed. to appear in Mathematische Zeitschrift