Revista de la
Unión Matemática Argentina
On commutative homogeneous vector bundles attached to nilmanifolds
Rocío Díaz Martín and Linda Saal
Volume 62, no. 1 (2021), pp. 141–151

Download PDF


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.