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