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

Abstract

Let X = G/B be the full flag variety associated to a symmetrizable Kac–Moody group G . Let T be the maximal torus of G . The T -equivariant K -theory of X has a certain natural basis defined as the dual of the structure sheaves of the finite-dimensional Schubert varieties. We show that under this basis, the structure constants are polynomials with nonnegative coefficients. This result in the finite case was obtained by Anderson–Griffeth–Miller (following a conjecture by Graham–Kumar).