Compatibility of the Theta correspondence with the Whittaker functors
Abstract
We prove that the global geometric theta-lifting functor for the pair (H, G) is compatible with the Whittaker normalization, where (H,G) is one of the pairs (SO2n, Sp2n), (Sp2n, SO2n+2) or (GLn,GLn+1). That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H.
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