Triply imprimitive representations of GL(2)

Schmidt, Ralf; Turki, Salam

doi:10.1090/proc/13803

Triply imprimitive representations of GL(2)
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by Ralf Schmidt and Salam Turki PDF

Proc. Amer. Math. Soc. 146 (2018), 971-981 Request permission

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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