A local converse theorem for Sp(2r)

作者:Zhang; Qing
来源:Mathematische Annalen, 2018, 372(1-2): 451-488.
DOI:10.1007/s00208-017-1623-2

摘要

In this paper, we prove the local converse theorem for Sp(2r) (F) over a p-adic field F. More precisely, given two irreducible supercuspidal representations of Sp(2r) (F) with the same central character such that they are generic with the same additive character and they have the same gamma factors when twisted with generic irreducible representations of GL(n)(F) for all 1 <= n <= r, then these two representations must be isomorphic. Our proof is based on the local analysis of the local integrals which define local gamma factors. A key ingredient of the proof is certain partial Bessel function property developed by Cogdell-Shahidi-Tsai recently. The same method can give the local converse theorem for U(r, r).