## 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.

Original language | English |
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Pages (from-to) | 22-66 |

Number of pages | 45 |

Journal | Advances in Mathematics |

Volume | 243 |

DOIs | |

Publication status | Published - 2013 Aug 20 |

Externally published | Yes |

## Keywords

- Equivariant K-theory
- Isotropic Grassmannians
- Schubert class
- Schur Q-functions

## ASJC Scopus subject areas

- Mathematics(all)