Matching realization of $U_q(s{l}_{n+1})$ of higher rank in the quantum Weyl algebra ${\mathcal{W}}_q(2n)$

In the paper, we further realize the higher rank quantized universal enveloping algebra $U_q(s{l}_{n+1})$ as certain quantum differential operators in ${\mathcal{W}}_q(2n)$ defined over the quantum divided power algebra ${\mathcal{A}}_q(n)$ of rank $n$. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of $U_q(s{l}_{n+1})$. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.