Abstract
We study unitarity of the induced representations from coisotropic quantum subgroups which were introduced by Ciccoli in math.QA/9804138. We define a real structure on coisotropic subgroups which determines an involution on the homogeneous space. We give general invariance properties for functionals on the homogeneous space which are sufficient to build a unitary representation starting from the induced one. We present the case of the one-dimensional quantum Galilei group where we have to use in all generality our definition of quasi-invariant functional.
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Bonechi, F., Ciccoli, N., Giachetti, R. et al. Unitarity of Induced Representations from Coisotropic Quantum Subgroups. Letters in Mathematical Physics 49, 17–31 (1999). https://doi.org/10.1023/A:1007678630817
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DOI: https://doi.org/10.1023/A:1007678630817