Matching realization of U_q(sl_n+1) of higher rank in the quantum Weyl algebra W_q(2n)

In the paper, we further realize the higher rank quantized universal enveloping algebra U_q(sl_n+1) as certain quantum differential operators in the quantum Weyl algebra W_q(2n) defined over the quantum divided power algebra 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(sl_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.