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

Abstract

We prove sign-alternation of the structure constants in the basis of the structure sheaves of opposite Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the flag varieties G / P G/P associated to an arbitrary symmetrizable Kac-Moody group G G , where P P is any parabolic subgroup. This generalizes the work of Anderson-Griffeth-Miller from the finite case to the general Kac-Moody case, and affirmatively answers a conjecture of Lam-Schilling-Shimozono regarding the signs of the structure constants in the case of the affine Grassmannian.