A theta operator for the group \(\mathrm{GSp}_4\)

We construct a differential operator on sheaves of \(p\)-adic modular forms defined over the locus of \(p\)-rank \(\ge 1\) of the Siegel threefold, by applying a revisited version of the approach that Sean Howe recently introduced in his paper "A unipotent circle action on \(p\)-adic modular forms" (2020, Trans. Am. Math. Soc.) to construct the theta operator in the elliptic case.