Dual enhanced Shahidi conjecture for unramified Arthur-type representations
Dual enhanced Shahidi conjecture for unramified Arthur-type representations
Let be a connected reductive group over a non-Archimedean local field , and let . Assume that a theory of local Arthur packets for exists. For a local Arthur parameter , let be its associated local -parameter; an Arthur-type representation is one lying in some local Arthur packet, and an unramified representation is one with a nonzero hyperspecial-fixed vector. Dual enhanced Shahidi conjecture. Every unramified Arthur-type representation of lies in exactly one local Arthur packet, and that packet is associated with an anti-generic local Arthur packet. Moreover, if is unramified, then contains a unique unramified representation, namely the representation associated with through the Satake isomorphism. The source says this is proved for quasi-split classical groups and for in the paper, while the general connected reductive case remains open.
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Primary source
Alexander Hazeltine, Baiying Liu and Chi-Heng Lo, “On the enhanced Shahidi conjecture and global applications”, arXiv:2404.05773 (2024).
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