K-theoretic analogues of factorial Schur P- and Q-functions
By Takeshi Ikeda, H. Naruse. 2011
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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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6523e4c38ba28708ec3a7aad4291c5437e844a39
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
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