Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II

摘要

We prove sign-alternation of the structure constants in the basis ofstructure sheaves of opposite Schubert varieties in the torus-equivariantGrothendieck group of coherent sheaves on the flag varieties $G/P$ associatedto an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolicsubgroup. This generalizes the work of Anderson-Griffeth-Miller from the finitecase to the general Kac-Moody case, and affirmatively answers a conjecture ofLam-Schilling-Shimozono regarding the signs of the structure constants in thecase of the affine Grassmannian.