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

Takeshi Ikeda*, Hiroshi Naruse

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


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 languageEnglish
Pages (from-to)22-66
Number of pages45
JournalAdvances in Mathematics
Publication statusPublished - 2013 Aug 20
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics


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