3 problems

Let $\tilde\pi$ be an Iwahori $p$-refinement of a RASCAR of $\mathrm{GL}_4$. The refinement may be optimally $B$-spin, $Q$-spin, or $G$-spin, where $B$, $Q$, and $G$ are respective…

Let $\tilde\pi$ be a $p$-refined RASCAR of $\mathrm{GL}_{2n}$, and let $P_{\tilde\pi}$ be the associated parabolic. A symplectic family is a family through $\tilde\pi$ in the eigen…

For a spherical cuspidal representation of $\mathrm{GL}_4$ with its $p$-refinements, a symplectic family is understood modulo one-dimensional trivial variation. Symplectic-family d…