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Double-bosonization and Majid’s Conjecture (II): irregular R-matrices and type-crossing to G2

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Abstract

The purpose of the paper is to build up the related theory of weakly quasitriangular dual pairs suitably for non-standard R-matrices (irregular), and establish the generalized double-bosonization construction for irregular R, which generalizes Majid’s results for regular R’s in [M1]. As an application, the type-crossing construction for the exceptional quantum group of type G2 is given explicitly. This affirms Majid’s expectation that the tree structure of nodes diagram associated with quantum groups can be grown out of the node corresponding to \({U_q}({\mathfrak{sl}_2})\) by the (generalized) double-bosonization procedures.

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Acknowledgements

The authors are greatly indebted to the referee for his or her invaluable comments and insights on our manuscript which made the expressions of our ideas on the theme more precise. The first author is partially supported by the Natural Science Research projects of universities in Jiangsu Province (Grant No. 18KJB110027) and the NNSFC (Grant No. 11801394); the second author is partially supported by the NNSFC (Grant Nos. 11771142 and 12071094) and in part by the Science and Technology Commission of Shanghai Municipality (Grant No. 18dz2271000).

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Authors and Affiliations

  1. School of Mathematical Sciences, Suzhou University of Science and Technology, Shihu Campus, Ke Rui Road 1, Suzhou, 215009, PR China

    Hongmei Hu

  2. School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Minhang Campus, Dong Chuan Road 500, Shanghai, 200241, PR China

    Naihong Hu

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  1. Hongmei Hu
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  2. Naihong Hu
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Correspondence to Naihong Hu.

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Hu, H., Hu, N. Double-bosonization and Majid’s Conjecture (II): irregular R-matrices and type-crossing to G2. Isr. J. Math. 244, 901–943 (2021). https://doi.org/10.1007/s11856-021-2197-y

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  • DOI: https://doi.org/10.1007/s11856-021-2197-y

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