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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 132, Number 10, Pages 28752883
S 0002-9939(04)07424-6
Article electronically published on May 12, 2004
DISTINGUISHED REPRESENTATIONS
AND POLES OF TWISTED TENSOR L-FUNCTIONS
U. K. ANANDAVARDHANAN, ANTHONY C. KABLE, AND R. TANDON
(Communicated by Wen-Ching Winnie Li)
Abstract. Let E/F be a quadratic extension of p-adic 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 L-function 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.

  

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

 

Collections: Mathematics