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 < 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.
Categories: math.RT