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Matching realization of U q (sl n+1) of higher rank in the quantum Weyl algebra W q (2n)

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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 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.

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Authors and Affiliations

  1. Department of Mathematics and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, P. R. China

    Nai Hong Hu & Shen You Wang

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  1. Nai Hong Hu
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  2. Shen You Wang
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Correspondence to Shen You Wang.

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Supported by National Natural Science Foundation of China (Grant No. 11271131)

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Hu, N.H., Wang, S.Y. Matching realization of U q (sl n+1) of higher rank in the quantum Weyl algebra W q (2n). Acta. Math. Sin.-English Ser. 30, 1674–1688 (2014). https://doi.org/10.1007/s10114-014-3721-3

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  • DOI: https://doi.org/10.1007/s10114-014-3721-3

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