more conceptual argument. We revisit this construction in §\[section:examples\]. Ultimately, we hope that this article will clarify once and for all a variety of issues that occur when leaving the relative safety of ${\operatorname{GL}}_n$, giving a firm framework for further research on Galois representations into groups other than ${\operatorname{GL}}_n$.

Acknowledgements.
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We would like to thank Jeff Adams, James Arthur, Frank Calegari, Brian Conrad, Matthew Emerton, Wee Teck Gan, Dick Gross, Florian Herzig, Robert Langlands, David Loeffler, Ambrus Pál, Richard Taylor and David Vogan for helpful discussions relating to this work. Particular thanks go to Gross, for giving us a copy of Deligne’s letter to Serre and urging us to read it, and to Adams and Vogan for dealing with several questions of ours involving local Langlands at infinity which were apparently “known to the experts” but which we could not extract from the literature ourselves.

The first author was supported by an EPSRC Advanced Research Fellowship, and the second author would like to acknowledge the support of the National Science Foundation (award number DMS-0841491). He would also like to thank the mathematics department of Northwestern University for its hospitality in the early stages of this project.

$L$-groups and local 