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We revisit the local metaplectic correspondence previously constructed andstudied by Flicker and Kazhdan. After restoring and generalizing some of theirresults, we get several interesting applications to the representation theoryof a Kazhdan-Patterson covering group over a $p$-adic field, including a fullcriterion of the irreducibility of the Bernstein-Zelevinsky product of twocuspidal representations, the classification of essentially square integrableand tempered representations, and more interestingly, the calculation of theWhittaker dimension of an irreducible representation.

Local metaplectic correspondence and applications