Construction of modules for Lie superalgebras of type \(C\) (Q1899094)

Simple modules of the Lie superalgebra \(C_n\) have been classified by \textit{V. G. Kac} [Lect. Notes Math. 676, 597-626 (1977; Zbl 0388.17002)], who also gave character formulae for typical modules; for the remaining atypical modules character formulae were given in [\textit{J. Van der Jeugt}, Commun. Algebra 19, No. 1, 199-222 (1991; Zbl 0721.17004)]. In a certain sense, this makes the representation theory for \(C_n\) complete. In the present paper, the problem of constructing simple modules as submodules of \(W= \otimes^f V\), with \(V\) the natural representation of \(C_n\), is considered. This analysis is along the lines of the work of \textit{A. Berele} and \textit{A. Regev} [Adv. Math. 64, 118-175 (1987; Zbl 0617.17002)]. Using Young symmetrizers and graded contractions, maximal vectors \(v\) of \(W\) are constructed. Certain simple modules of \(C_n\) can then be identified with \({\mathcal U} (C_n) v\).