Restrictions of SL3 Maass Forms to Maximal Flat Subspaces

We assume that ‖ψ‖2 = 1. We also assume that the spectral parameter of ψ is of the form tλ, where t> 1 and λ ∈ B∗, and B∗ is a fixed compact regular subset of a∗. Let Ω ⊆ X be a compact set. Let E ⊂Ω be a ball of radius 1 inside a maximal flat subspace of S. It was proved in [14, Theorem 1.2] that ‖ψ |E‖2 B∗,Ω t3/4, and moreover that this bound is sharp on the compact globally symmetric space SU(3)/SO(3) which is dual to S. Note that [6, Theorem 3] and the L∞ bound of [16] also provide bounds of