#### 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 $M{p}_{2n}$ 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
Primary: 22E35