  We study the properties of a thermodynamic system having the symmetry of a
quantum group and interacting with a harmonic potential. We calculate the
dependence of the chemical potential, heat capacity and spatial distribution of
the gas on the quantum group parameter $q$ and the number of spatial dimensions
$D$. In addition, we consider a fourth-order interaction in the quantum group
fields $\Psi$, and calculate the ground state energy up to first order.
