Subconvexity for sup-norms of cusp forms on $$mathrm{PGL}(n)$$

Let F be an (L^2)-normalized Hecke Maaß cusp form for (Gamma _0(N) subseteq {mathrm{SL}}_{n}({mathbb {Z}})) with Laplace eigenvalue (lambda _F). If (Omega ) is a compact subset of (Gamma _0(N)backslash {mathrm{PGL}}_n/mathrm{PO}_{n}), we show the bound (Vert F|_{Omega }Vert _{infty } ll _{ Omega } N^{varepsilon } lambda _F^{n(n-1)/8 - delta }) for some constant (delta = delta _n> 0) depending only on n.