Composition series of a class of induced representations, a case of one half cuspidal reducibility

Igor Ciganović

Vol. 296 (2018), No. 1, 21–30

DOI: 10.2140/pjm.2018.296.21

Abstract

We determine the composition series of the induced representation

$$\delta \left(\left[{\nu }^{-b}\rho ,{\nu }^c\rho \right]\right)\times \delta \left(\left[{\nu }^{\frac{1}{2}}\rho ,{\nu }^a\rho \right]\right)⋊\sigma ,$$

where $a,b,c\in \frac{1}{2}\left(2\mathbb{Z}+1\right)$ satisfy $\frac{1}{2}\le a<b<c$, $\rho$ is an irreducible cuspidal unitary representation of a general linear group and $\sigma$ is an irreducible cuspidal representation of a classical group.

Keywords

classical group, composition series, discrete series, generalized principal representation, $p$-adic field, Jacquet module

Mathematical Subject Classification 2010

Primary: 22E50

Secondary: 11F85, 22D30

Milestones

Received: 30 August 2017

Revised: 24 October 2017

Accepted: 24 January 2018

Published: 1 May 2018