<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>K</mml:mi></mml:math>-theoretic analogues of factorial Schur<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mi>P</mml:mi></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.gif" display="inline" overflow="scroll"><mml:mi>Q</mml:mi></mml:math>-functions

DOI DOI Web Site Web Site 10 Citations 22 References Open Access

Description

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.

Final version

Journal

Citations (10)*help

See more

References(22)*help

See more

Related Projects

See more

Keywords

Report a problem

Back to top