  We study a simple model of a quantum Hall system with the electrons confined
to a linear, narrow channel. The system is mapped to a 1D system which in the
low-energy approximation has the form of a Luttinger liquid with different
interactions between particles of equal and of opposite chiralities. We study
this mapping at the microscopic level, and discuss the relation between the
parameters of the 2D system and the corresponding 1D Luttinger liquid
parameters. We focus in particular on how the parameters are renormalized by
the electron interactions and show that the velocity parameter of the current
is not modified by the interaction.
