Induction from two linked segments with one half border and cuspidal reducibility

TL;DR

This paper determines the composition series of a specific induced representation involving linked segments with one half border and cuspidal reducibility, advancing understanding of representation structures in classical groups.

Contribution

It explicitly computes the composition series of induced representations with linked segments and cuspidal reducibility, a novel detailed analysis in this context.

Findings

Explicit composition series for the induced representation.

Identification of reducibility points for the induced representations.

Enhanced understanding of the structure of induced representations in classical groups.

Abstract

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