The Einstein condition for quantum irreducible flag manifolds

Abstract

We show that any quantum irreducible flag manifold satisfies an analogue of the Einstein condition, expressing proportionality between the Ricci tensor and the metric, at least in a small open interval around the classical value of the quantization parameter. This makes use of various canonical constructions associated to these algebras, such as differential calculi and bimodule connections, which were previously introduced by various authors.