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The image of complex conjugation in \(l\)-adic representations associated to automorphic forms. (English) Zbl 1303.11065

Summary: 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 \( \mathrm{GL}_n(\mathbb A_{F^+})\), then we calculate the image of any complex conjugation under the \(l\)-adic representations \(r_{l,\iota}(\Pi)\) associated to \(\Pi\).

MSC:

11F80 Galois representations
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