2011/12/31 by Takeshi Ikeda, Hiroshi Naruse · 1 citation
Mathematics · #math.CO #math.AG #math.KT #math.RT #msc:05E05 #msc:14M15 #msc:19L47
paper · pdf · doi:10.1016/j.aim.2013.04.014
published as Advances in Mathematics 243 (2013), 22--66 · Final version
arxiv created 2013/05/24 · arxiv updated 2013/05/27
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, 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.