4 problems

Let $L\subseteq L_1$ be a sublattice, let $A$, $B(L)$, $K_1$, $H_1(L)$, $L^\perp$, and $\psi_1^w$ be as defined in the lattice model, and let $r_2$ be the associated exponent. Seco…

Let $L\subseteq L_1$ be a sublattice, let $S_L$ be the associated subspace in the lattice model, and let $J_1(L)^\circ$ and $J_2(M)^\circ$ be the compact subgroups defined from the…

Let $F$ be a non-archimedean local field of characteristic $0$, let $W$ be a symplectic space over $F$, and let $(U(\mathcal{V}_1),U(\mathcal{V}_2))$ be an irreducible dual reducti…

Let $p$ be prime, let $\rho$ be the Weil representation factoring through $Sp=SL_{2}(\mathbb{F}_{p})$, and let $A\in Sp$. Write $T_A$ for the centralizer of $A$, let…