Double Grothendieck polynomials for symplectic and odd orthogonal Grassmannians

Thomas Hudson; Takeshi Ikeda; Tomoo Matsumura; Hiroshi Naruse

doi:10.1016/j.jalgebra.2019.11.002

Double Grothendieck polynomials for symplectic and odd orthogonal Grassmannians

Thomas Hudson, Takeshi Ikeda, Tomoo Matsumura, Hiroshi Naruse

Research output: Contribution to journal › Article

Abstract

We study the double Grothendieck polynomials of Kirillov–Naruse for the symplectic and odd orthogonal Grassmannians. These functions are explicitly written as Pfaffian sum form and are identified with the stable limits of fundamental classes of the Schubert varieties in torus equivariant connective K-theory of these isotropic Grassmannians. We also provide a combinatorial description of the ring formally spanned be the double Grothendieck polynomials.

Original language	English
Pages (from-to)	294-314
Number of pages	21
Journal	Journal of Algebra
Volume	546
DOIs	https://doi.org/10.1016/j.jalgebra.2019.11.002
Publication status	Published - 2020 Mar 15
Externally published	Yes

Keywords

Equivariant K-theory
Isotropic Grassmannians
Pfaffian
Schubert class

ASJC Scopus subject areas

Algebra and Number Theory

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AU - Hudson, Thomas

AU - Ikeda, Takeshi

AU - Matsumura, Tomoo

AU - Naruse, Hiroshi

PY - 2020/3/15

Y1 - 2020/3/15

N2 - We study the double Grothendieck polynomials of Kirillov–Naruse for the symplectic and odd orthogonal Grassmannians. These functions are explicitly written as Pfaffian sum form and are identified with the stable limits of fundamental classes of the Schubert varieties in torus equivariant connective K-theory of these isotropic Grassmannians. We also provide a combinatorial description of the ring formally spanned be the double Grothendieck polynomials.

AB - We study the double Grothendieck polynomials of Kirillov–Naruse for the symplectic and odd orthogonal Grassmannians. These functions are explicitly written as Pfaffian sum form and are identified with the stable limits of fundamental classes of the Schubert varieties in torus equivariant connective K-theory of these isotropic Grassmannians. We also provide a combinatorial description of the ring formally spanned be the double Grothendieck polynomials.

KW - Equivariant K-theory

KW - Isotropic Grassmannians

KW - Pfaffian

KW - Schubert class

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