The non-Abelian Duality Problem
  We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that hinges on two key observations: (i) from the point of view of dualities, whether the group of symmetries of a model is or is not Abelian is unimportant, and (ii) the new theory of dualities that we exploit includes traditional duality transformations, but also introduces in a natural way more general transformations. 
E. Cobanera, G. Ortiz, and E. Knill
cond-mat.stat-mech hep-th math-ph math.MP quant-ph