Quantum exceptional group G_2 and its semisimple conjugacy classes

We construct quantization of semisimple conjugacy classes of the exceptional group G = G2 along with and by means of their representations on highest weight modules over the quantum group Uq(g). With every point t of a fixed maximal torus we associate a highest weight module Mt over Uq(g) and realize the quantized polynomial algebra of the class of t by linear operators on Mt . Quantizations corresponding to points of the same orbit of the Weyl group are isomorphic.