Alternating formulas for K -theoretic quiver polynomials

Abstract

The main theorem here is the $K$-theoretic analogue of the cohomological ``stable double component formula'' for quiver polynomials in [KMS]. This $K$-theoretic version is still in terms of lacing diagrams, but nonminimal diagrams contribute terms of higher degree. The motivating consequence is a conjecture of Buch [B1] on the sign alternation of the coefficients appearing in his expansion of quiver $K$-polynomials in terms of stable Grothendieck polynomials for partitions.