8 problems

Let $\mu$ be a splitting character used to define the oscillator–Heisenberg representation, and let…

Gan–Gross–Prasad's Fourier–Jacobi conjecture. There is exactly one pair $\pi_V\in\Pi^{\mathrm{Vogan}}_{\varphi_V}$ and…

Let $q$ be a power of a prime $p\neq 2$, let $\psi:\mathbb F_q\to\mathbb{\bar Q}_\ell^\times$ be a nontrivial additive character, and let $G_n=\mathrm U_n$ or $\mathrm{Sp}_{2n}$. F…

Induced-representation multiplicity formula. In the Bessel cases, for possibly reducible induced representations

Hiss–Schröer's conjecture. The multiplicities $m(\pi,\sigma)$ of the irreducible constituents of $\pi\otimes\omega_\psi^\vee$ are bounded by a function of $n$ independent of $q$.

Let $k$ be a local field. Let $J={\mathrm{SL}}_2(k)\ltimes V$ be the subgroup of the split group ${\mathrm{G}}_2(k)$ described above, let $\widetilde{\mathrm{SL}}_2(k)$ be the meta…

Let $\phi$ be a generic $L$-parameter of $U(n)\times U(n)$, and let $\Pi^R_{\phi}$ be its relevant Vogan $L$-packet. A representation in this packet is said to produce the Fourier-…

Let $G_n$ be a unitary-group pair with relevant pure inner forms $G_n'$ and diagonal subgroup $H_n'$, and let $\Pi^R_{\phi}$ be the relevant Vogan $L$-packet associated to an $L$-p…