Compatibility of the Theta correspondence with the Whittaker functors

Vincent Lafforgue (1) , Sergey Lysenko (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Whittaker functor; Geometric Langlands; theta-lifting

Domaines: Mathématiques [math]

Vincent Lafforgue, Sergey Lysenko. Compatibility of the Theta correspondence with the Whittaker functors. Bulletin de la société mathématique de France, 2011, 139 (1), pp.75-88. ⟨10.24033/bsmf.2600⟩. ⟨hal-01144801⟩