We determine the Verma multiplicities of standard filtrations of projective modules for integral atypical blocks in the BGG category O for the orthosymplectic Lie superalgebras osp(3|4) by way of translation functors. We then explicitly determine the composition factor multiplicities of Verma modules using BGG reciprocity.

We examine Atiyah’s Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D topological quantum field theories (TQFTs) and Frobenius algebras, we find the algebraic objects corresponding to Hermitian and unitary TQFTs, respectively, and prove structure theorems about them. We then clarify a few older results on unitary TQFTs using our structure theorems.