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

Takeshi Ikeda*, Hiroshi Naruse

*この研究の対応する著者

研究成果: Article査読

37 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)22-66
ページ数45
ジャーナルAdvances in Mathematics
243
DOI
出版ステータスPublished - 2013 8 20
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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