Supercharacters and superdimensions of irreducible representations of B(O/s) orthosymplectic simple Lie superalgebras. (English) Zbl 0702.17003
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 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.
Reviewer: J.Van der Jeugt
MSC:
| 17A70 | Superalgebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B70 | Graded Lie (super)algebras |
Keywords:
supercharacters; superdimensions; irreducible representations; orthosymplectic Lie superalgebraCitations:
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