We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order $n$. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.
Principal series representations of metaplectic groups over local fields
On extensions of principal series representations
Singularities of Intertwining Operators and Decompositions of Principal Series Representations
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