Motivated by mirror symmetry and Langlands duality we recall how filtered medium algebras can be understood both as equivariant cohomology of affine Schubert varieties and as endomorphism algebras in category O. We generalise this to quantum medium algebras and show in type A that they describe the equivariant K-theory of affine Schubert varieties and endomorphism algebras in quantum category O. The proof uses fixed point schemes and GKM theory for K-theory and the action of an affine Hecke algebra in quantum Schur-Weyl duality. Joint work with Jakub Löwit.