Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations

TL;DR

This paper proves that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, confirming a conjecture and deriving an Euler--Poincaré characteristic formula, while identifying a class of projective restrictions.

Contribution

It establishes the vanishing of Ext-analogues for tempered representations and confirms a conjecture, also identifying a class of representations with projective restrictions.

Findings

Ext-analogues vanish for tempered representations

Euler--Poincaré characteristic formula confirmed

Certain tempered representations have projective restrictions

Abstract

In this paper we prove that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, as conjectured by D. Prasad. In particular, this implies a conjectural Euler--Poincar\'e characteristic formula for Gan--Gross--Prasad models. Besides, we also single out a special class of tempered representations, which includes the Steinberg representation, and show that the restrictions of them are projective.