A theta operator for the group GSp4

We construct a differential operator on sheaves of [Formula: see text]-adic modular forms defined over the locus of [Formula: see text]-rank [Formula: see text] of the Siegel threefold, by applying a revisited version of the approach that Howe recently introduced in [S. Howe, A unipotent circle action on [Formula: see text]-adic modular forms, Trans. Am. Math. Soc. Ser. B 7(6) (2020) 186–226, doi:10.1090/btran/52.] to construct the theta operator in the elliptic case.