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arXiv · 2405.17375

Global long root $A$-packets for $\mathsf{G}_2$: the dihedral case

Petar Bakić·Aleksander Horawa·Siyan Daniel Li-Huerta·Naomi Sweeting
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Abstract

Cuspidal automorphic representations $\tau$ of $\mathrm{PGL}_2$ correspond to global long root $A$-parameters for $\mathsf{G}_2$. Using an exceptional theta lift between $\mathrm{PU}_3$ and $\mathsf{G}_2$, we construct the associated global $A$-packet and prove the Arthur multiplicity formula for these representations when $\tau$ 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 $\mathsf{G}_2$.

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Petar Bakić, Aleksander Horawa, Siyan Daniel Li-Huerta, Naomi Sweeting. 2024-05-27. Global long root $A$-packets for $\mathsf{G}_2$: the dihedral case. https://arxiv.org/abs/2405.17375

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