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).