Induced representations of the one-dimensional quantum Galilei group

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