Parabolic induction from two segments, linked under contragredient, with a one half cuspidal reducibility, a special case

Abstract

In this paper, we determine the composition series of the induced representation \(\delta([\nu^{-a}\rho,\nu^c\rho])\times \delta([\nu^\frac{1}{2}\rho,\nu^b\rho])\rtimes \sigma\) where \(a, b, c \in \mathbb{Z}+\frac{1}{2}\) such that \(\frac{1}{2}\leq a \le b \le c\), \(\rho\) is an irreducible cuspidal unitary representation of a general linear group and \(\sigma\) is an irreducible cuspidal representation of a classical group such that \(\nu^\frac{1}{2}\rho\rtimes \sigma\) reduces.