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| Matching Realization of Uq（sln＋1） of Higher Rank in the Quantum Weyl Algebra Wq（2n） | |
| 引用本文： | Nai Hong HU Shen You WANG. Matching Realization of Uq（sln＋1） of Higher Rank in the Quantum Weyl Algebra Wq（2n）[J]. 数学学报(英文版), 2014, 30(10): 1674-1688. DOI: 10.1007/s10114-014-3721-3 |
| 作者姓名： | Nai Hong HU Shen You WANG |
| 作者单位： | Department of Mathematics and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, P. R. China |
| 基金项目： | Supported by National Natural Science Foundation of China(Grant No.11271131) |
| 摘 要： | In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided power algebra Sq（n） of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq（sln＋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. |
| 关 键 词： | 量子代数 匹配 微分算子 包络代数 根向量 对称性 平方 |
Matching realization of U q (sl n+1) of higher rank in the quantum Weyl algebra W q (2n) |
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| Nai Hong Hu,Shen You Wang. Matching realization of U q (sl n+1) of higher rank in the quantum Weyl algebra W q (2n)[J]. Acta Mathematica Sinica(English Series), 2014, 30(10): 1674-1688. DOI: 10.1007/s10114-014-3721-3 | |
| Authors: | Nai Hong Hu Shen You Wang |
| Affiliation: | 1. Department of Mathematics and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, P. R. China |
| 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 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. |
| Keywords: | Quantum divided power algebra quantum differential operators quantum Weyl algebra Lusztig symmetries matching realization |
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