Langlands parameters and L-homomorphisms
The (local) goal of Langlands’ theory of L-groups is the description of representations of real forms of G in terms of an L-group of G. In this chapter we begin our detailed analysis of the parameters that will appear in this description, without as yet explaining how they are related to representation theory. As is explained in , E-groups play the same rôle with respect to the description of certain projective representations (corresponding always to linear covering groups) and they can be treated at the same time without difficulty. (Indeed it is apparent from Definitions 4.3 and 4.6 that E-groups are in certain respects less complicated than L-groups.) In any case we will need to have E-groups available when we discuss endoscopy.
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