Abstract

We show two results on local theta correspondence and restrictions of irreducible admissible representations of GL(2) over p-adic fields. Let F be a nonarchimedean local field of characteristic 0, and let L be a quadratic extension of F. Let ε_{L ∕ F} is the character of F^× corresponding to the extension L ∕ F, and let GL₂(F)⁺ be the subgroup of GL₂(F) consisting of elements with ε_{L ∕ F}(detg) = 1. The first result is that the theorem of Moen–Rogawski on the theta correspondence for the dual pair (U(1),U(1)) is equivalent to a result by D. Prasad on the restriction to GL₂(F)⁺ of the principal series representation of GL₂(F) associated with 1,ε_{L ∕ F}. As the second result, we show that we can deduce from this a theorem of D. Prasad on the restrictions to GL₂(F)⁺ of irreducible supercuspidal representations of GL₂(F) associated to characters of L^×.

Keywords

theta correspondence, epsilon factor

Mathematical Subject Classification

Primary: 22E50, 11F27

Secondary: 11F70

Authors