In the paper, we further realize the higher rank quantized universal enveloping algebra U q (sl n+1 ) as certain quantum differential operators in 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.

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