Knapp–Stein dimension theorem for finite central covering groups

Caihua Luo

Vol. 306 (2020), No. 1, 265–280

DOI: 10.2140/pjm.2020.306.265

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 $M{p}_{2n}$ based on Gan and Savin’s work on the local theta correspondence for $\left(M{p}_{2n},{SO}_{2n+1}\right)$.

Keywords

finite central covering group, $R$-group, intertwining operator, Knapp–Stein dimension theorem

Mathematical Subject Classification 2010

Primary: 22E35

Milestones

Received: 10 November 2019

Revised: 21 December 2019

Accepted: 21 December 2019

Published: 14 June 2020