Non-tempered Ext Branching Laws for the $p$-adic General Linear Group

Abstract

Let $F$ be a non-archimedean local field. Let $\ddot{I}{€}_1$ and $\ddot{I}{€}_2$ be irreducible Arthur type representations of ${\mathrm{GL}}_n(F)$ and ${\mathrm{GL}}_{n-1}(F)$ respectively. We study Ext branching laws when $\ddot{I}{€}_1$ and $\ddot{I}{€}_2$ are products of discrete series representations and their Aubert-Zelevinsky duals. We obtain an Ext analogue of the local non-tempered Gan-Gross-Prasad conjecture in this case.

Revised version; to appear in IMRN