Knapp–Stein dimension theorem for finitecentral covering groups

Abstract

It is folklore that the Knapp-Stein dimension theorem should be extended word by word to general covering groups. But we note that such a proof does not exist in the literature. For completeness, we provide a proof of the classical Knapp-Stein dimension theorem for finite central covering groups. As an example, we obtain the R-group structure for Mp(2n) based on Gan and Savin's work on the local theta correspondence for (Mp(2n), SO2n+1).

Topics & Concepts