Abstract
In a recent paper characters and superdimension formulas were investigated for the class of representations with Dynkin labels \([0,\ldots ,0,p]\) of the Lie superalgebra \(\mathfrak {osp}(m|n)\). Such representations are infinite-dimensional, and of relevance in supergravity theories provided their superdimension is finite. We have shown that the superdimension of such representations coincides with the dimension of a \(\mathfrak {so}(m-n)\) representation. In the present contribution, we investigate how this \(\mathfrak {osp}(m|n)\sim \mathfrak {so}(m-n)\) correspondence can be extended to the class of \(\mathfrak {osp}(2m|2n)\) representations with Dynkin labels \([0,\ldots ,0,q,p]\).
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Acknowledgements
NIS and JVdJ were supported by the Joint Research Project “Lie superalgebras - applications in quantum theory” in the framework of an international collaboration programme between the Research Foundation – Flanders (FWO) and the Bulgarian Academy of Sciences. NIS was partially supported by the Bulgarian National Science Fund, grant DN 18/1. This research (JT-M) was supported in part by the Intramural Research Program of the NIH, U.S. National Library of Medicine.
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Stoilova, N.I., Thierry-Mieg, J., Van der Jeugt, J. (2018). On Superdimensions of Some Infinite-Dimensional Irreducible Representations of \(\mathfrak {osp}(m|n)\). In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 . LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 263. Springer, Singapore. https://doi.org/10.1007/978-981-13-2715-5_9
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DOI: https://doi.org/10.1007/978-981-13-2715-5_9
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