q-Painlevé VI Equation Arising from q-UC Hierarchy

We study the q-difference analogue of the sixth Painlevé equation (q-P_VI) by means of tau functions associated with the affine Weyl group of type D₅. We prove that a solution of q-P_VI coincides with a self-similar solution of the q-UC hierarchy. As a consequence, we obtain in particular algebraic solutions of q-P_VI in terms of the universal character which is a generalization of the Schur polynomial attached to a pair of partitions.