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Prasad–Kaletha conjecture on refined parameters of contragredient packets
Prasad–Kaletha conjecture. The refined Langlands parameter for each representation $\pi^\vee$ in $\Pi_\varphi^\vee(G)$ can be explicitly determined.
Conjectureopencontragredient-representations local-langlands refined-l-parametersarXiv posted 2 days ago

Prasad–Kaletha conjecture on refined parameters of contragredient packets