Inverse<i>K</i>-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type

Abstract We prove an explicit inverse Chevalley formula in the equivariant K -theory of semi-infinite flag manifolds simply laced type. By ‘inverse formula’ we mean a for product scalar with Schubert class, expressed as $\mathbb {Z}\left [q^{\pm 1}\right ]$ -linear combination classes twisted by line bundles. Our applies to arbitrary type and scalars $e^{\lambda }$ , where $\lambda $ is minuscule weight. result Stembridge, our completely determines weights except $E_8$ . The combinatorics governed quantum Bruhat graph, proof based on limit from double affine Hecke algebra. Thus also provides determination all nonsymmetric q -Toda operators ADE