Harmonic Analysis and Gamma Functions on Symplectic Groups R. A. McWilliam From the construction of the

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Harmonic Analysis and Gamma Functions on Symplectic Groups R. A. McWilliam From the construction of theOver a p adic local field F of characteristic zero, we develop a new type of harmonic analysis on an extended symplectic group G = Gm x Sp2n. It is associated to the Langlands ? functions attached to any irreducible admissible representations ? ? ? of G(F) and the standard representation ? of the dual group G?(C), and confirms a series of the conjectures in the local theory of the Braverman Kazhdan proposal (Braverman and Kazhdan, 2000) for the case