Unitary representations of basic classical Lie superalgebras
Among the basic classical Lie superalgebras, gl(m/n) and C(n) are the only ones admitting finite-dimensional unitary irreducible representations; these unitary representations are sometimes called the star representations [\textit{M. Scheunert}, \textit{W. Nahm} and \textit{V. Rittenberg}, J. Math. Phys. 18, 146-154 (1977; Zbl 0354.17004)]. In this paper, the necessary and sufficient conditions on the highest weight \(\Lambda\) of a finite-dimensional simple module V(\(\Lambda\)) are given for V(\(\Lambda\)) to be unitary. The lowest weights of such unitary irreducible representations can be worked out explicitly (even in the case when V(\(\Lambda\)) is atypical). The covariant, resp. contravariant, tensor representations of gl(m/n), appearing in the tensor product of the standard gl(m/n) module (resp. the dual of the standard module), are shown to be unitary.
scientific article; zbMATH DE number 4177344
scientific article