Cuspidal automorphic representations τ of PGL₂ correspond to global long root A-parameters for G₂. Using an exceptional theta lift between PU₃ and G₂, we construct the associated global A-packet and prove the Arthur multiplicity formula for these representations when τ is dihedral and satisfies some technical hypotheses. We also prove that this subspace of the discrete automorphic spectrum forms a full near equivalence class. Our construction yields new examples of quaternionic modular forms on G₂.
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Bakić et al. (2024) studied this question.
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