ON COMMUTATIVE HOMOGENEOUS VECTOR BUNDLES ATTACHED TO NILMANIFOLDS

The notion of Gelfand pair (G,K) can be generalized by considering homogeneous vector bundles over G/K instead of the homogeneous space G/K and matrix-valued functions instead of scalar-valued functions. This gives the definition of commutative homogeneous vector bundles. Being a Gelfand pair is a necessary condition for being a commutative homogeneous vector bundle. In the case when G/K is a nilmanifold having square-integrable representations, a big family of commutative homogeneous vector bundles was determined in [Transform. Groups 24 (2019), no. 3, 887-911]. In this paper we complete that classification.