Excited Young diagrams and equivariant Schubert calculus

Takeshi Ikeda, Hiroshi Naruse

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

We describe the torus-equivariant cohomology ring of isotropic Grassmannians by using a localization map to the torus fixed points. We present two types of formulas for equivariant Schubert classes of these homogeneous spaces. The first formula involves combinatorial objects which we call "excited Young diagrams", and the second one is written in terms of factorial Schur Q- or P-functions. As an application, we give a Giambelli-type formula for the equivariant Schubert classes. We also give combinatorial and Pfaffian formulas for the multiplicity of a singular point in a Schubert variety.

Original languageEnglish
Pages (from-to)5193-5221
Number of pages29
JournalTransactions of the American Mathematical Society
Volume361
Issue number10
DOIs
Publication statusPublished - 2009 Oct
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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