 
Summary: PACIFIC JOURNAL OF MATHEMATICS
Vol. 206, No. 2, 2002
ON DISTINGUISHEDNESS
U.K. Anandavardhanan and R. Tandon
Let F be a finite extension of Qp and K a quadratic ex
tension of F . If (, 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 is said to be µdistinguished with re
spect to H if there exists a nonzero linear form l on V such
that l((g)v) = µ(det g)l(v) for g H and v V . We provide
new proofs, using entirely local methods, of some wellknown
results in the theory of nonarchimedean distinguished repre
sentations for GL(2).
1. Introduction.
Let K/F be a quadratic extension of nonarchimedean local fields of char
acteristic zero. For a local field F, OF will be the ring of integers of F
and PF the maximal ideal of OF . Let F be a generator of PF . Let vF
be the valuation of F such that vF (F ) = 1. The cardinality of OF /PF is
denoted by qF . Let be the nontrivial element of the Galois group of K
