Compatibility of the Theta correspondence with the Whittaker functors
arXiv:0902.0051 · doi:10.24033/bsmf.2600
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 (SO_{2n}, Sp_{2n}), (Sp_{2n}, SO_{2n+2}) or (GL_{n},GL_{n+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.
13 pages, final version to appear in Bulletin SMF