#### Vol. 6, No. 3, 2012

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The image of complex conjugation in $l$-adic representations associated to automorphic forms

### Richard Taylor

Vol. 6 (2012), No. 3, 405–435
##### Abstract

If ${F}^{+}$ is a totally real field, if $n$ is an odd integer and if $\Pi$ is a regular, algebraic, essentially self-dual, cuspidal automorphic representation of ${GL}_{n}\left({\mathbb{A}}_{{F}^{+}}\right)$, then we calculate the image of any complex conjugation under the $l$-adic representations ${r}_{l,\iota }\left(\Pi \right)$ associated to $\Pi$.

##### Keywords
Galois representations
Primary: 11F80