2 problems

Generation conjecture. Let $T(B)$ be the algebra generated by $T^k(a_1,\ldots,a_k)$ where $a_1,a_2,\ldots,a_k\in B$ and $k\in\mathbb{Z}_{+}$. Then

Let $\mathcal{P}_\lambda$ and $\mathcal{P}_\mu$ be positive representations of the split real quantum group $\mathcal{U}_{q\widetilde{q}}(\mathfrak{g}_{\mathbb{R}})$, and let…