A note on special orthogonal groups following Waldspurger

Abstract

The purpose of this note is to verify that the archimedean multiplicity one theorems shown for orthogonal groups (as well as general linear and unitary groups) in a previous paper of the authors remain valid for special orthogonal groups. The necessary ingredients to establish this variant are due to Waldspurger.

This note is incorporated into the article "Multiplicity one theorems: the Archimedean case", arXiv:0903.1413, to appear in Annals of Mathematics