Two remarks on a theorem of Dipendra Prasad

Hiroshi Saito
2008 Pacific Journal of Mathematics  
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 L/F is the character of F × corresponding to the extension L/F, and let GL 2 (F) + be the subgroup of GL 2 (F) consisting of elements with L/F (det g) = 1. The first result is that the theorem of Moen-Rogawski on the theta correspondence for the dual pair
more » ... (1), U(1)) is equivalent to a result by D. Prasad on the restriction to GL 2 (F) + of the principal series representation of GL 2 (F) associated with 1, L/F . As the second result, we show that we can deduce from this a theorem of D. Prasad on the restrictions to GL 2 (F) + of irreducible supercuspidal representations of GL 2 (F) associated to characters of L × .
doi:10.2140/pjm.2008.234.185 fatcat:bqosgorxjjdp7o7onlgdxtngqu