Bonechi, F.; Giachetti, R.; Sorace, E.; Tarlini, M. Induced representations of the one-dimensional quantum Galilei group. (English) Zbl 0905.17009 Lett. Math. Phys. 43, No. 4, 309-318 (1998). 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. Cited in 2 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory Keywords:induced representations; quantum Galilei group; Kirillov method; irreducible representations; one-dimensional lattice PDFBibTeX XMLCite \textit{F. Bonechi} et al., Lett. Math. Phys. 43, No. 4, 309--318 (1998; Zbl 0905.17009) Full Text: DOI