2 problems

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Gaitsgory–Kazhdan irreducibility conjecture for induced representations
Gaitsgory–Kazhdan irreducibility conjecture. The object $\Pi\in \operatorname{Rep}(\BG)$ is irreducible.
Conjectureopeninduced-representations loop-groups representation-theoryarXiv posted 2 days ago
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Salamanca-Vogan conjecture on induction from unitarily small representations
Let $G$ be a real reductive group, and call an irreducible unitary representation $\pi\in\Pi_{\Lambda}(G)$ unitarily small if $\Lambda$ lies in the convex hull of…
Conjecturerefutedinduced-representations unitary-representationsarXiv posted 2 days ago

Gaitsgory–Kazhdan irreducibility conjecture for induced representations