Double Schubert polynomials for the classical groups

Takeshi Ikeda, Leonardo C. Mihalcea, Hiroshi Naruse

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

For each infinite series of the classical Lie groups of type B, C or D, we construct a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the appropriate flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomials of Billey and Haiman, which represent non-equivariant Schubert classes. They are also positive in a certain sense, and when indexed by maximal Grassmannian elements, or by the longest element in a finite Weyl group, these polynomials can be expressed in terms of the factorial analogues of Schur's Q- or P-functions defined earlier by Ivanov.

Original languageEnglish
Pages (from-to)840-886
Number of pages47
JournalAdvances in Mathematics
Volume226
Issue number1
DOIs
Publication statusPublished - 2011 Jan 15
Externally publishedYes

Keywords

  • Double Schubert polynomials
  • Equivariant cohomology
  • Factorial P or Q-Schur

ASJC Scopus subject areas

  • Mathematics(all)

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