Vol. 306, No. 1, 2020

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Knapp–Stein dimension theorem for finite central covering groups

Caihua Luo

Vol. 306 (2020), No. 1, 265–280
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 Mp2n based on Gan and Savin’s work on the local theta correspondence for (Mp2n,SO2n+1).

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
Authors
Caihua Luo
Department of Mathematical Sciences
Chalmers University of Technology
Goteborg
Sweden