Double Schubert polynomials for the classical Lie groups

Takeshi Ikeda, Leonardo Mihalcea, Hiroshi Naruse

Research output: Contribution to conferencePaper

1 Citation (Scopus)

Abstract

For each infinite series of the classical Lie groups of type B, C or D, we introduce 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 corresponding 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. When indexed by maximal Grassmannian elements of the Weyl group, these polynomials are equal to the factorial analogues of Schur Q- or P-functions defined earlier by Ivanov.

Original languageEnglish
Pages665-676
Number of pages12
Publication statusPublished - 2008
Externally publishedYes
Event20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile
Duration: 2008 Jun 232008 Jun 27

Other

Other20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
CountryChile
CityValparaiso
Period08/6/2308/6/27

Keywords

  • Factorial Q-function
  • Flag variety
  • Schubert polynomial

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Ikeda, T., Mihalcea, L., & Naruse, H. (2008). Double Schubert polynomials for the classical Lie groups. 665-676. Paper presented at 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08, Valparaiso, Chile.