Super dual pairs and highest weight modules of orthosymplectic algebras
For a symplectic Lie group \(\text{Sp} (2n,\mathbb{R})\), all unitary lowest (or highest) weight representations can be realized as a subrepresentation in some power of tensor products of the Weil representation (also known as the oscillator representation). In the present paper this result is extended to the orthosymplectic Lie superalgebra \(\text{osp} (2n, m; \mathbb{R})\). A complete result is obtained only for \(\text{osp} (2,2; \mathbb{R})\), but also for the general case interesting results are proved. The method used in this paper is based upon the notion of super dual pairs, following Lie algebra dual pairs of \textit{R. Howe} [Bull. Am. Math. Soc., New Ser. 3, 821-843 (1980; Zbl 0442.43002)].
orthosymplectic Lie superalgebra \(\text{osp} (2n, m
scientific article; zbMATH DE number 611209