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Decomposing oscillator representations of \({\mathfrak osp}(2n/n;{\mathbb{R}{}})\) by a super dual pair \({\mathfrak osp}(2/1;{\mathbb{R}{}}) \times{} {\mathfrak so}(n)\). (English) Zbl 0741.17002
The oscillator representation of the Lie superalgebra \(\text{osp}(2n/n;\mathbb{R})\) is introduced, and is shown to be a unitary representation. It is shown that \(\text{osp}(2n/n;\mathbb{R})\) contains a super dual pair \(\text{osp}(2/1;\mathbb{R})\times\text{so}(n)\). The decomposition of the oscillator representation into irreducible representations of \(\text{osp}(2/1;\mathbb{R})\times\text{so}(n)\) is solved, and some interesting byproducts in superanalysis are obtained.

MSC:
17A70 Superalgebras
17B70 Graded Lie (super)algebras
22E70 Applications of Lie groups to the sciences; explicit representations
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