Pfaffian sum formula for the symplectic Grassmannians

Takeshi Ikeda*, Tomoo Matsumura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)269-306
Number of pages38
JournalMathematische Zeitschrift
Volume280
Issue number1-2
DOIs
Publication statusPublished - 2015 Jun 1
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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