Abstract
We give a general theory for the construction of oscillator-like unitary irreducible representations (UIRs) of non-compact supergroups in a super Fock space. This construction applies to all non-compact supergroupsG whose coset spaceG/K with respect to their maximal compact subsupergroupK is “Hermitean supersymmetric”. We illustrate our method with the example of SU(m, p/n+q) by giving its oscillator-like UIRs in a “particle state” basis as well as “supercoherent state basis”. The same class of UIRs can also be realized over the “super Hilbert spaces” of holomorphic functions of aZ variable labelling the coherent states.
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Communicated by J. Lascoux
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Bars, I., Günaydin, M. Unitary representations of non-compact supergroups. Commun.Math. Phys. 91, 31–51 (1983). https://doi.org/10.1007/BF01206048
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DOI: https://doi.org/10.1007/BF01206048