A vanishing Ext-branching theorem for $({\mathrm{GL}}_{n+1}(F),{\mathrm{GL}}_n(F))$

Abstract

We prove a conjecture of Dipendra Prasad on the Ext-branching problem from ${\mathrm{GL}}_{n+1}(F)$ to ${\mathrm{GL}}_n(F)$, where $F$ is a $p$-adic field.

18 pages, v2: expand introduction, improve results in Section 2, and the appendix is rewritten