Location of reducibility points of induced representations I: A toy example

Abstract

By analyzing the singularity of standard intertwining operators, we provide a new way to understand the explicit location of reducibility points of induced representations of two Speh representations for general linear groups over a p-adic field. Through playing with this toy example, it seems that the analytic approach, in the spirit of Mœglin--Waldspurger, could play a role for analogous reducibility problems in the setting of classical groups. On the other hand, it also stimulates the arising of some interesting questions.