Supercharacters and superdimensions of irreducible representations of B(O/s) orthosymplectic simple Lie superalgebras (Q914815)

Formulae for supercharacters and superdimensions of simple modules (or irreducible representations) of the orthosymplectic Lie superalgebra \(B(0/s)=osp(1/2s)\) are derived. The basic paper on representations of Lie superalgebras was written by \textit{V. G. Kac} [Lect. Notes Math. 676, 597- 626 (1978; Zbl 0388.17002)]. However, as the authors point out, some errors were published in this paper for the case of B(0/s). In the present note, the authors reconstruct the supercharacter and superdimension formulae. First, some general properties of B(0/s) are given. Then, following the analysis of Kac, the supercharacter is correctly rederived. Finally, using a limit procedure originally due to Weyl, the formula for the superdimension is obtained.