Extension of the \(\mathfrak{osp}(m|n)\sim \mathfrak{so}(m-n)\) correspondence to the infinite-dimensional chiral spinors and self dual tensors. (English) Zbl 1364.81278
Summary: The spinor representations of the orthosymplectic Lie superalgebras \(\mathfrak{osp}(m|n)\) are considered and constructed. These are infinite-dimensional irreducible representations, of which the superdimension coincides with the dimension of the spinor representation of \(\mathfrak{so}(m-n)\). Next, we consider the self dual tensor representations of \(\mathfrak{osp}(m|n)\) and their generalizations: these are also infinite-dimensional and correspond to the highest irreducible component of the \(p\)th power of the spinor representation. We determine the character of these representations, and deduce a superdimension formula. From this, it follows that also for these representations the \(\mathfrak{osp}(m|n)\sim \mathfrak{so}(m-n)\) correspondence holds.
MSC:
| 81V80 | Quantum optics |
| 81T10 | Model quantum field theories |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81Q70 | Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory |
| 17A70 | Superalgebras |
Keywords:
orthosymplectic Lie superalgebras; spinor and self dual tensor representations; superdimensionsReferences:
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