Composition series for degenerate principal series of GL(n)

TL;DR

This paper investigates the structure of certain representations of GL(n) over local fields, focusing on their reducibility and composition series, providing a unified proof and exploring applications in integral geometry.

Contribution

It offers a short, uniform proof of the composition series for degenerate principal series of GL(n), extending previous results to a broader setting.

Findings

Established reducibility criteria for these representations

Described the composition series explicitly

Connected results to applications in cosine transforms

Abstract

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.