Double Schubert polynomials for the classical Lie groups

Takeshi Ikeda; Leonardo Mihalcea; Hiroshi Naruse

Double Schubert polynomials for the classical Lie groups

Takeshi Ikeda^*, Leonardo Mihalcea, Hiroshi Naruse

^*Corresponding author for this work

Research output: Contribution to conference › Paper › peer-review

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 language	English
Pages	665-676
Number of pages	12
Publication status	Published - 2008
Externally published	Yes
Event	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: 2008 Jun 23 → 2008 Jun 27

Other

Other	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
Country/Territory	Chile
City	Valparaiso
Period	08/6/23 → 08/6/27

Keywords

Factorial Q-function
Flag variety
Schubert polynomial

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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title = "Double Schubert polynomials for the classical Lie groups",

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.",

keywords = "Factorial Q-function, Flag variety, Schubert polynomial",

author = "Takeshi Ikeda and Leonardo Mihalcea and Hiroshi Naruse",

year = "2008",

language = "English",

pages = "665--676",

note = "20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 ; Conference date: 23-06-2008 Through 27-06-2008",

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TY - CONF

T1 - Double Schubert polynomials for the classical Lie groups

AU - Ikeda, Takeshi

AU - Mihalcea, Leonardo

AU - Naruse, Hiroshi

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Factorial Q-function

KW - Flag variety

KW - Schubert polynomial

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M3 - Paper

AN - SCOPUS:84860472289

SP - 665

EP - 676

T2 - 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08

Y2 - 23 June 2008 through 27 June 2008

ER -

Double Schubert polynomials for the classical Lie groups

Abstract

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Keywords

ASJC Scopus subject areas

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