Revista de la Unión Matemática Argentina Home Editorial board For authors Latest issue In press MCA 2021 Online first Prize Search OJS

### Published volumes

##### 1936-1944
On commutative homogeneous vector bundles attached to nilmanifolds
Volume 62, no. 1 (2021), pp. 141–151

### Abstract

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.