Distinguished representations and poles of twisted tensor functions
Authors:
U. K. Anandavardhanan, Anthony C. Kable and R. Tandon
Journal:
Proc. Amer. Math. Soc. 132 (2004), 28752883
MSC (2000):
Primary 11F70, 11F85
Published electronically:
May 12, 2004
MathSciNet review:
2063106
Fulltext PDF Free Access
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Abstract: Let be a quadratic extension of adic fields. If is an admissible representation of that is parabolically induced from discrete series representations, then we prove that the space of invariant linear functionals on has dimension one, where is the mirabolic subgroup. As a corollary, it is deduced that if is distinguished by , then the twisted tensor function associated to has a pole at . 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 . 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.
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Additional Information
U. K. Anandavardhanan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400 005, India
Email:
anand@math.tifr.res.in
Anthony C. Kable
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email:
akable@math.okstate.edu
R. Tandon
Affiliation:
Department of Mathematics and Statistics, University of Hyderabad, Hyderabad 500 046, India
Email:
rtsm@uohyd.ernet.in
DOI:
http://dx.doi.org/10.1090/S0002993904074246
PII:
S 00029939(04)074246
Keywords:
Distinguished representations,
local twisted tensor $L$function,
Asai $L$function,
BernsteinZelevinsky derivatives
Received by editor(s):
September 11, 2002
Received by editor(s) in revised form:
June 3, 2003
Published electronically:
May 12, 2004
Communicated by:
WenChing Winnie Li
Article copyright:
© Copyright 2004
American Mathematical Society
