Double Grothendieck polynomials for symplectic and odd orthogonal Grassmannians

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.