Dual Groups and Langlands Functoriality

J. W. Cogdell

Chapter 11 in An Introduction to the Langlands Program, 2004, pp 251-268 from Springer

Abstract: Abstract Langlands never separated the Langlands conjectures for GL n from his general principle of functoriality [30]. In particular, he formulated a correspondence between certain Galois representations and admissible or automorphic representations for any connected reductive algebraic group G. For GL n there was a correspondence between certain n-dimensional Galois representations, that is, representations into GL n (ℂ), and admissible representations of GL n (k) or automorphic representations of GL n (A) [4]. For general G we understand what to replace the automorphic side with: admissible representations of G(k) or automorphic rep-resentations of G(A).

Date: 2004
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DOI: 10.1007/978-0-8176-8226-2_11

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