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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 (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.
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https://hal.archives-ouvertes.fr/hal-01144801
Contributor : Vincent Lafforgue <>
Submitted on : Wednesday, April 22, 2015 - 4:49:41 PM
Last modification on : Tuesday, October 23, 2018 - 4:48:08 PM

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  • HAL Id : hal-01144801, version 1
  • ARXIV : 0902.0051

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Vincent Lafforgue, Sergey Lysenko. Compatibility of the Theta correspondence with the Whittaker functors. Bulletin de la SMF, 2011, 139 (1), pp.75-88. ⟨hal-01144801⟩

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