Title: Modular representations in type A with a two-row nilpotent central character,
Abstract: We study the category of representations of $\mathfrak{sl}_{m+2n}$ in
positive characteristic, whose p-character is a nilpotent whose Jordan type is
the two-row partition (m+n,n). In a previous paper with Anno, we used
Bezrukavnikov-Mirkovic-Rumynin's theory of positive characteristic localization
and exotic t-structures to give a geometric parametrization of the simples
using annular crossingless matchings. Building on this, here we give
combinatorial dimension formulae for the simple objects, and compute the
Jordan-Holder multiplicities of the simples inside the baby Vermas (in special
case where n=1, i.e. that a subregular nilpotent, these were known from work of
Jantzen). We use Cautis-Kamnitzer's geometric categorification of the tangle
calculus to study the images of the simple objects under the [BMR] equivalence.
The dimension formulae may be viewed as a positive characteristic analogue of
the combinatorial character formulae for simple objects in parabolic category O
for $\mathfrak{sl}_{m+2n}$, due to Lascoux and Schutzenberger.