Israel Journal of Mathematics

, Volume 123, Issue 1, pp 317–340

Quadratic base change of θ10


DOI: 10.1007/BF02784134

Cite this article as:
Kim, J. & Piatetski-Shapiro, I.I. Isr. J. Math. (2001) 123: 317. doi:10.1007/BF02784134


In case ofGLn overp-adic fields, it is known that Shintani base change is well behaved. However, things are not so simple for general reductive groups. In the first part of this paper, we present a counterexample to the existence of quadratic base change descent for some Galois invariant representations. These are representations of type θ10. In the second part, we compute the localL-factor of θ10. Unlike many other supercuspidal representations, we find that theL-factor of θ10 has two poles. Finally, we discuss these two results in relation to the local Langlands correspondence.

Copyright information

© The Hebrew University Magnes Press 2001

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA