Pairings between Cartan subgroups and the proof of Theorem 10.4
Theorem 12.3 describes representations in terms of Cartan subgroups of G Γ, and Theorem 12.9 describes Langlands parameters in terms of Cartan subgroups of ∨ G Γ. To complete the proof of Theorem 10.4, we need to relate Cartan subgroups of G Γ and ∨ G Γ. We begin by doing this for maximal tori. The following lemma more or less restates the definition of dual group; we leave its proof to the reader.
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