The non-abelian target space duals of Taub-NUT space

We discuss the non-abelian duality procedure for groups which do not act freely. As an example we consider Taub-NUT space, which has the local isometry group $SU(2) \otimes U(1)$. We dualise over the entire symmetry group as well as the subgroups $SO(3)$ and $U(1)$, presenting unusual new solutions to low energy string theory. The solutions obtained highlight the relationship between fixed points of an isometry in one solution and singular points in another. We also find the interesting results that, in this case, the $U(1)$ and $SO(3)$ $T$-duality procedures commute with each other, and that the extreme points of the $O(1,1)$ duality group for the time translations have special significance under the $SO(3)$ T-duality.