The local theta correspondence conjecture for quaternionic dual pairs
Local theta correspondence conjecture. If s∈Sϕ+s\in S_\phi^+s∈Sϕ+ and s′∈Sϕ′+s'\in S_{\phi'}^+s′∈Sϕ′+ are associated via ξ\xiξ, and π∈Πϕ(G(V))\pi\in\Pi_\phi(G(V))π∈Πϕ(G(V)), then θψ(π,W)\theta_\psi(\pi,W)θψ(π,W) has LLL-parameter…