Formula omitted]-theoretic analogues of factorial Schur [formula omitted]- and [formula omitted]-functions

Abstract

We introduce two families of symmetric functions generalizing the factorial Schur P- and Q-functions due to Ivanov. We call them K-theoretic analogues of factorial Schur P- and Q-functions. We prove various combinatorial expressions for these functions, e.g. as a ratio of Pfaffians, a sum over set-valued shifted tableaux, and a sum over excited Young diagrams. As a geometric application, we show that these functions represent the Schubert classes in the K-theory of torus equivariant coherent sheaves on the maximal isotropic Grassmannians of symplectic and orthogonal types. This generalizes a corresponding result for the equivariant cohomology given by the authors. We also discuss a remarkable property enjoyed by these functions, which we call the K-theoretic Q-cancellation property. We prove that the K-theoretic P-functions form a (formal) basis of the ring of functions with the K-theoretic Q-cancellation property.