Weight-aspect sup-norm conjecture for Hecke eigenforms on Siegel modular varieties

Let $F$ be a Siegel cusp form of degree $n$ and weight $k$ on the group under consideration, normalized with respect to the Petersson norm, and suppose that $F$ is an eigenfunction of all Hecke operators. Define

$$\lVert F\rVert_\infty:=\sup_{Z=X+iY\in\mathbf H_n}\det(Y)^{k/2}|F(Z)|.$$

Weight-aspect sup-norm conjecture. If $F$ is an eigenfunction of all Hecke operators, then as $k\to\infty$,

$$\lVert F\rVert_\infty\ll k^{n(n+1)/8}.$$

This conjecture seeks a bound for an individual eigenform matching the scale suggested by average lower bounds and dimension considerations. The source presents it as an expected bound, with level-one Ikeda lifts as motivation; it remains open in the stated generality.