Compatibility of the Theta correspondence with the Whittaker functors
Representation Theory
2023-08-25 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.0902.0051,
title = {Compatibility of the Theta correspondence with the Whittaker functors},
author = {Vincent Lafforgue and Sergey Lysenko},
journal= {arXiv preprint arXiv:0902.0051},
year = {2023}
}
Comments
13 pages, final version to appear in Bulletin SMF