4 problems

Generic Summand Conjecture. There exists a cuspidal realization ${\mathcal {C}}_\pi$ with first occurrence index $\ell_0$ and a suitable $k$-rational orbit…

Bessel-period obstruction conjecture. The integer $\ell$, with $0\leq\ell\leq {\mathfrak {r}}_n$, is not the first occurrence index of $\pi$.

Liu's refined global Gross–Prasad conjecture. One has

Special case of global Gan–Gross–Prasad. If there is an automorphic form $\phi$ in the space of $\pi$ such that $B(\phi,\Lambda)\neq0$, then