3 problems

Let $G$ be a connected reductive group over a local field with Lie algebra $\frak{g}$, let $L$ be a sufficiently large extension of ${\mathbb Q}_p$ over which $G$ is split, and let…

Galois-infinitesimal character conjecture. The center $Z(\mathfrak{g})$ acts on this representation via $\zeta^C_\rho$.

0–1 coefficient conjecture. One must have $n_i=0$ or $1$ for every $1\leq i\leq l$.