We realize the irreducible representations of a compact Lie supergroup G, with a contragredient simple Lie superalgebra, in the space of square integrable (in the sense of Berezin) holomorphic sections on X=GA, A is the real torus in the complexification of G. We give an explicit realization of unitary representations when G=SU(1|1).
Chuah, M.-K., Cremonini, C.A., Fioresi, R. (2024). Harmonic analysis of compact Lie supergroups. EXPOSITIONES MATHEMATICAE, 1, 1-13 [10.1016/j.exmath.2024.125586].
Harmonic analysis of compact Lie supergroups
Fioresi R.
2024
Abstract
We realize the irreducible representations of a compact Lie supergroup G, with a contragredient simple Lie superalgebra, in the space of square integrable (in the sense of Berezin) holomorphic sections on X=GA, A is the real torus in the complexification of G. We give an explicit realization of unitary representations when G=SU(1|1).File in questo prodotto:
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