 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 132, Number 10, Pages 28752883
S 00029939(04)074246
Article electronically published on May 12, 2004
DISTINGUISHED REPRESENTATIONS
AND POLES OF TWISTED TENSOR LFUNCTIONS
U. K. ANANDAVARDHANAN, ANTHONY C. KABLE, AND R. TANDON
(Communicated by WenChing Winnie Li)
Abstract. Let E/F be a quadratic extension of padic fields. If is an ad
missible representation of GLn(E) that is parabolically induced from discrete
series representations, then we prove that the space of Pn(F )invariant linear
functionals on has dimension one, where Pn(F ) is the mirabolic subgroup.
As a corollary, it is deduced that if is distinguished by GLn(F ), then the
twisted tensor Lfunction associated to has a pole at s = 0. It follows that
if is a discrete series representation, then at most one of the representations
and is distinguished, where is an extension of the local class field
theory character associated to E/F . This is in agreement with a conjecture
of Flicker and Rallis that relates the set of distinguished representations with
the image of base change from a suitable unitary group.
