Product type actions of GqGq

We will study a faithful product type action of GqGq, the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T   of GqGq. This enables us to classify product type actions of SUq(2)SUq(2) up to conjugacy. We also compute the intrinsic group of Gq,ΩGq,Ω, the 2-cocycle deformation of GqGq that is naturally associated with the quantum flag manifold L∞(T\Gq)L∞(T\Gq).