Abstract: The local theta correspondence does not preserve L-packets. As a remedy, Adams conjectured that instead of L-packets, the theta correspondence preserves Arthur packets. Moeglin verified Adams' conjecture when the theta correspondence has sufficiently large rank. Moeglin also showed that Adams' conjecture fails in low rank. Bakic and Hanzer showed that the failure can be managed: namely if Adams conjecture holds at some rank then it holds in any higher rank. In this talk, we discuss how to understand the failure of Adams' conjecture in low rank and how to remedy it.
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