On distinguishedness

U.K. Anandavardhanan and R. Tandon

Vol. 206 (2002), No. 2, 269–286

DOI: 10.2140/pjm.2002.206.269

Abstract

Let F be a finite extension of Q_p and K a quadratic extension of F. If (Π,V ) is a representation of GL₂(K), H a subgroup of GL₂(K) and μ a character of the image subgroup det(H) of K^∗, then Π is said to be μ-distinguished with respect to H if there exists a nonzero linear form l on V such that l(Π(g)v) = μ(detg)l(v) for g ∈ H and v ∈ V . We provide new proofs, using entirely local methods, of some well-known results in the theory of non-archimedean distinguished representations for GL(2).

Milestones

Received: 11 January 2001

Revised: 28 November 2001

Published: 1 October 2002