  In this note we consider representations of the group GL(n,F), where F is the
field of real or complex numbers or, more generally, an arbitrary local field,
in the space of equivariant line bundles over Grassmannians over the same field
F. We study reducibility and composition series of such representations.
  Similar results were obtained already in [HL99,Al12,Zel80], but we give a
short uniform proof in the general case, using the tools from [AGS15a]. We also
indicate some applications to cosine transforms in integral geometry.
