Mathematische Zeitschrift

, Volume 280, Issue 1–2, pp 269–306 | Cite as

Pfaffian sum formula for the symplectic Grassmannians

Article

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.

Keywords

Schubert classes Symplectic Grassmannians Torus equivariant cohomology Giambelli type formula Wilson’s conjecture Double Schubert polynomials 

Mathematics Subject Classification

Primary 14M15 Secondary 05E05 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Applied MathematicsOkayama University of ScienceOkayamaJapan
  2. 2.Department of Mathematical SciencesKAISTDaejeonSouth Korea

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