Splitting metaplectic covers of dual reductive pairs

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The symplectic group Sp(N, F) over a local fieldF (other than ℂ) has a unique non-trivial twofold central extension. The inclusion of {±1} into the circle ℂ1 induces an extension\(1 \to C^1 \to Mp(n,F) \to Sp(n,F) \to \). In this paper, an explicit splitting of the restriction of this extension to a dual reductive pair (G, H) in Sp(n, F) is given in all cases in which it exists. Such an explicit splitting is often an essential technical ingredient in the study of the local theta correspondence for the dual pair [4].