Triply imprimitive representations of GL(2)
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- by Ralf Schmidt and Salam Turki PDF
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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.References
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Additional Information
- Ralf Schmidt
- Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-3103
- MR Author ID: 636524
- 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
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 971-981
- MSC (2010): Primary 11F70, 22E50
- DOI: https://doi.org/10.1090/proc/13803
- MathSciNet review: 3750211