Distinguished dihedral representations of GL(2) over a p-adic field

Nadir Matringe

Distinguished dihedral representations of GL(2) over a p-adic field

Representation Theory 2007-05-23 v3

Authors: Nadir Matringe

Abstract

Let $F$ be a finite extension of ${\mathbb{Q}} \_p$ . Any dihedral supercuspidal representation of $GL \_2 (K)$ arises from an admissible multiplicative character $\omega$ of a quadratic extension $L$ of $K$ . We show that such a representation is distinguished for $GL \_2 (F)$ if and only if $L$ biquadratic over $F$ and $\omega$ restricted to invertibles of one of the two other quadratic extensions of $F$ in $L$ is trivial. We then observe a similar statement for the principal series and we study all dihedral representations.

Keywords

dihedral representations gl(2) p-adic field supercuspidal representations distinguished representations quadratic extensions

Cite

@article{arxiv.math/0610724,
  title  = {Distinguished dihedral representations of GL(2) over a p-adic field},
  author = {Nadir Matringe},
  journal= {arXiv preprint arXiv:math/0610724},
  year   = {2007}
}

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