Equivariant schubert calculus and jeu DE taquin

Hugh Thomas, Alexander Yong

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce edge labeled Young tableaux. Our main results provide a corresponding analogue of Schützenberger's theory of jeu de taquin. These are applied to the equivariant Schubert calculus of Grassmannians. Reinterpreting, we present new (semi)standard tableaux to study factorial Schur polynomials, after Biedenharn-Louck, Macdonald, Goulden-Greene, and others. Consequently, we obtain new combinatorial rules for the Schubert structure coefficients, complementing work of Molev-Sagan, Knutson-Tao, Molev, and Kreiman. We also describe a conjectural generalization of one of our rules to the equivariant K-theory of Grassmannians, extending our previous work on non-equivariant K-theory. This conjecture concretely realizes the “positivity” known to exist by a result of Anderson-Gri eth-Miller. It provides an alternative to the conjectural rule of Knutson-Vakil.

Original languageEnglish (US)
Pages (from-to)275-318
Number of pages44
JournalAnnales de l'Institut Fourier
Volume68
Issue number1
DOIs
StatePublished - 2018

Keywords

  • Equivariant cohomology
  • Grassmannians
  • Jeu de taquin
  • Schubert calculus

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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