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arXiv · 1401.8184

Matching realization of $U_q(sl_{n+1})$ of higher rank in the quantum Weyl algebra $\mathcal W_q(2n)$

Naihong Hu·Shenyou Wang
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Abstract

In the paper, we further realize the higher rank quantized universal enveloping algebra $U_q(sl_{n+1})$ 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 $U_q(sl_{n+1})$. 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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Naihong Hu, Shenyou Wang. 2014-01-31. Matching realization of $U_q(sl_{n+1})$ of higher rank in the quantum Weyl algebra $\mathcal W_q(2n)$. https://doi.org/10.1007/s10114-014-3721-3

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