Geometry of Quantum Group invariant systems

Starting with the partition functions for quantum group invariant systems we calculate the metric in the two-dimensional space defined by the parameters $\beta$ and $\gamma=-\beta\mu$ and the corresponding scalar curvature for these systems in two and three spatial dimensions. Our results exhibit the details of the anyonic behavior of quantum group boson and fermion systems as a function of the fugacity $z$ and the quantum group parameter $q$. For the case of the quantum group $SU_q(2)$, we compare the stability of these systems with the stability of SU(2) invariant boson and fermion systems.