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PACIFIC JOURNAL OF MATHEMATICS Vol. 206, No. 2, 2002
 

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 a character of the image subgroup
det(H) of K
, then is said to be -distinguished with re-
spect to H if there exists a nonzero linear form l on V such
that l((g)v) = (det g)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 repre-
sentations for GL(2).
1. Introduction.
Let K/F be a quadratic extension of non-archimedean 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

  

Source: Anandavardhanan, U. K. - Department of Mathematics, Indian Institute of Technology Bombay

 

Collections: Mathematics