Global long root $A$-packets for $\mathsf{G}_2$: the dihedral case
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914079223840768 |
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| author | Bakić, Petar Horawa, Aleksander Li-Huerta, Siyan Daniel Sweeting, Naomi |
| author_facet | Bakić, Petar Horawa, Aleksander Li-Huerta, Siyan Daniel Sweeting, Naomi |
| contents | Cuspidal automorphic representations $τ$ 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 $τ$ 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 $\mathsf{G}_2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_17375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global long root $A$-packets for $\mathsf{G}_2$: the dihedral case Bakić, Petar Horawa, Aleksander Li-Huerta, Siyan Daniel Sweeting, Naomi Number Theory Representation Theory 11F70 (Primary) 11F27 (Secondary) Cuspidal automorphic representations $τ$ 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 $τ$ 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 $\mathsf{G}_2$. |
| title | Global long root $A$-packets for $\mathsf{G}_2$: the dihedral case |
| topic | Number Theory Representation Theory 11F70 (Primary) 11F27 (Secondary) |
| url | https://arxiv.org/abs/2405.17375 |