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Triply imprimitive representations of GL(2)


Authors: Ralf Schmidt and Salam Turki
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 11F70, 22E50
DOI: https://doi.org/10.1090/proc/13803
Published electronically: October 10, 2017
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Abstract: We give a criterion for an irreducible, admissible, supercuspidal representation $ \pi $ of $ \mathrm {GL}(2,K)$, where $ K$ is a $ p$-adic field, to become a principal series representation under every quadratic base change. We determine all such $ \pi $ that have trivial central character and conductor $ 2$, and explain their relevance for the theory of elliptic curves.


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Additional Information

Ralf Schmidt
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-3103
Email: rschmidt@math.ou.edu

Salam Turki
Affiliation: Mathematics and Computer Science Department, Rhode Island College, 600 Mount Pleasant Avenue, Providence, RI 02908
Email: sturki@ric.edu

DOI: https://doi.org/10.1090/proc/13803
Received by editor(s): December 31, 2016
Received by editor(s) in revised form: April 21, 2017
Published electronically: October 10, 2017
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society