Matching Realization of Higher Rank in the Quantum Weyl Algebra

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.