Double Grothendieck Polynomials for Symplectic and Odd Orthogonal Grassmannians

TL;DR

This paper investigates double Grothendieck polynomials for symplectic and odd orthogonal Grassmannians, providing explicit Pfaffian sum formulas, their connection to Schubert classes, and a combinatorial ring description.

Contribution

It introduces explicit Pfaffian sum formulas for these polynomials and links them to stable limits of Schubert classes in equivariant connective K-theory.

Findings

Explicit Pfaffian sum formulas derived

Identification with stable limits of Schubert classes

Combinatorial description of the polynomial ring

Abstract

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