TY - JOUR

T1 - K-theoretic analogues of factorial Schur P- and Q-functions

AU - Ikeda, Takeshi

AU - Naruse, Hiroshi

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/8/20

Y1 - 2013/8/20

N2 - 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.

AB - 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.

KW - Equivariant K-theory

KW - Isotropic Grassmannians

KW - Schubert class

KW - Schur Q-functions

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U2 - 10.1016/j.aim.2013.04.014

DO - 10.1016/j.aim.2013.04.014

M3 - Article

AN - SCOPUS:84877898988

VL - 243

SP - 22

EP - 66

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -