  The main result of this paper is the construction of a new class of weight
shifting operators, similar to the theta operators of arXiv:1902.10911,
arXiv:1712.06969 and others, which are defined on the lower Ekedahl-Oort strata
of the geometric special fibre of unitary Shimura varieties of signature $(n-1,
1)$ at a good prime $p$, split in the in the reflex field $E$, which we assume
to be quadratic imaginary. These operators act on certain graded sheaves which
are obtained from the arithmetic structure of the EO strata, in particular the
$p$-rank on each stratum. We expect these operators to have applications to the
study of Hecke-eigensystems of modular forms modulo $p$ and generalisations of
the weight part of Serre's conjecture.
