The Arthur-closure conjecture for the unitary dual
The Arthur-closure conjecture for the unitary dual
Let ) be a non-Archimedean local field of characteristic zero, let be a connected reductive group over , and set . Let denote the unitary dual, let denote the Arthur representations, and let be the closure of under complementary series and unitary parabolic induction. Arthur-closure conjecture. Assuming the theory of local Arthur packets, the unitary dual is generated by the Arthur representations:
This conjecture proposes a construction of the whole unitary dual from Arthur representations and is stated for connected reductive groups over non-Archimedean local fields of characteristic zero. Its status is not resolved in the supplied text.
Sources & referencesView supporting material
Primary source
Alexander Hazeltine, Dihua Jiang, Baiying Liu, Chi-Heng Lo and Qing Zhang, “On the complementary Arthur representations and unitary dual for p-adic classical groups”, arXiv:2505.11381 (2026).
Additional references
3 papers in this index state this conjecture (2011–2025). The statement above is taken from the most recent of them; the others are arXiv:2410.11806, arXiv:1103.0043.
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