A Giambelli formula for even orthogonal Grassmannians

Anders Skovsted Buch, Andrew Kresch, Harry Tamvakis

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let X be an orthogonal Grassmannian parametrizing isotropic subspaces in an even dimensional vector space equipped with a nondegenerate symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in the classical and quantum cohomology rings of X as a polynomial in certain special Schubert classes. Our analysis reveals a surprising relation between the Schubert calculus on even and odd orthogonal Grassmannians. We also study eta polynomials, a family of polynomials defined using raising operators whose algebra agrees with the Schubert calculus on X.

Original languageEnglish (US)
Pages (from-to)17-48
Number of pages32
JournalJournal fur die Reine und Angewandte Mathematik
Volume2015
Issue number708
DOIs
StatePublished - Nov 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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