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Double-bosonization and Majid’s conjecture (IV): Type-crossings from A to BCD

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Abstract

Both in Majid’s double-bosonization theory and in Rosso’s quantum shuffle theory, the rankinductive and type-crossing construction for U q (g)’s is still a remaining open question. In this paper, working in Majid’s framework, based on the generalized double-bosonization theorem we proved before, we further describe explicitly the type-crossing construction of U q (g)’s for (BCD) n series directly from type A n−1 via adding a pair of dual braided groups determined by a pair of (R, R′)-matrices of type A derived from the respective suitably chosen representations. Combining with our results of the first three papers of this series, this solves Majid’s conjecture, i.e., any quantum group U q (g) associated to a simple Lie algebra g can be grown out of U q (sl2) recursively by a series of suitably chosen double-bosonization procedures.

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Authors and Affiliations

  1. Department of Mathematics, SKLPMMP, East China Normal University, Shanghai, 200241, China

    HongMei Hu & 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 (IV): Type-crossings from A to BCD . Sci. China Math. 59, 1061–1080 (2016). https://doi.org/10.1007/s11425-015-5119-9

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