Let $W$ be the Weyl group of an algebraic group $G$. The Artin braid group $Br_{\mathfrak{g}}$ is generated by the $T_i$ , $i \in I$ such that for all $i, j \in I$, \begin{align} \underbrace{T_i T_j \cdots}_{m_{ij}} = \underbrace{T_j T_i \cdots}_{m_{ij}}, \end{align} where $m_{ij}$ is the $(i,j)$-entry in the Coexter matrix of $G$. To each $w \in W$ one associates the element $T_w \in Br_{\mathfrak{g}}$ such that \begin{align} T_w = T_{i_1} \cdots T_{i_m}, \end{align} for each $\mathbf{i}=(i_1, \ldots, i_m) \in R(w)$, where $R(w) = \{(i_1, \ldots, i_m) : w = s_{i_1} \cdots s_{i_m}\}$.

Let $w_0$ be the longest word $W$. Then $T_{w_0 s_i}(F_i) = F_{i^*}$ and $T_i^{-1}(F_i)=-E_i$ by a result of Lusztig. Here $E_i, F_i \in U_q(\mathfrak{g})$, where $\mathfrak{g}$ is the Lie algebra of $G$. $i^* = \tau(i)$, $\tau$ is some isomorphism of the Dynkin diagram of $G$. I am not able to find this result in his book. Are there some references about this result? Thank you very much.

Let $W$ be the Weyl group of a simple algebraic group $G$. The Artin braid group $Br_{\mathfrak{g}}$ is generated by the $T_i$ , $i \in I$ such that for all $i, j \in I$, \begin{align} \underbrace{T_i T_j \cdots}_{m_{ij}} = \underbrace{T_j T_i \cdots}_{m_{ij}}, \end{align} where $m_{ij}$ is the $(i,j)$-entry in the Coxeter matrix of $W$. To each $w \in W$ one associates the element $T_w \in Br_{\mathfrak{g}}$ such that \begin{align} T_w = T_{i_1} \cdots T_{i_m}, \end{align} for each $\mathbf{i}=(i_1, \ldots, i_m) \in R(w)$, where $R(w) = \{(i_1, \ldots, i_m) : w = s_{i_1} \cdots s_{i_m}\}$.

Let $w_0$ be the longest element in $W$. Then $T_{w_0 s_i}(F_i) = F_{i^*}$ and $T_i^{-1}(F_i)=-E_i$ by a result of Lusztig. Here $E_i, F_i \in U_q(\mathfrak{g})$, where $\mathfrak{g}$ is the Lie algebra of $G$. $i^* = \tau(i)$, $\tau$ is some isomorphism of the Dynkin diagram of $G$. I am not able to find this result in his book. Are there some references about this result? Thank you very much.