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Abstract
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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
-group
structure for
based on Gan and Savin’s work on the local theta correspondence for
.
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Keywords
finite central covering group, $R$-group, intertwining
operator, Knapp–Stein dimension theorem
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Mathematical Subject Classification 2010
Primary: 22E35
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Milestones
Received: 10 November 2019
Revised: 21 December 2019
Accepted: 21 December 2019
Published: 14 June 2020
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