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Induced representations of the one-dimensional quantum Galilei group. (English) Zbl 0905.17009

Summary: The authors study the representations of the quantum Galilei group by a suitable generalization of the Kirillov method on spaces of noncommutative functions. On these spaces, they determine a quasi-invariant measure with respect to the action of the quantum group by which they discuss unitary and irreducible representations. The latter are equivalent to representations on \(\ell^2\), i.e. on the space of square summable functions on a one-dimensional lattice.

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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