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 \(U_{q}(\mathfrak {g})\). With every point t of a fixed maximal torus we associate a highest weight module M_t over \(U_{q}(\mathfrak {g})\) and realize the quantized polynomial algebra of the class of t by linear operators on M_t. Quantizations corresponding to points of the same orbit of the Weyl group are isomorphic.

中文翻译：

---

量子例外群G 2及其半简单共轭分类

我们构造了例外群G = G ₂的半简单共轭类的量化，并通过它们在量子群\（U_ {q}（\ mathfrak {g}）\）上的最高权重模块上的表示进行构造。与每一点吨的固定最大的环面我们最高权重模块关联中号_吨以上\（U_ {Q}（\ mathfrak {G}）\） ，实现类的的量化多项式代数吨由线性算子中号_吨。对应于Weyl基团相同轨道的点的量化是同构的。