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Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D

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Abstract

It is well-known that the Gauss decomposition of the generator matrix in the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. Defining relations between these generators are known in an explicit form, thus providing an isomorphism between the presentations. It has been an open problem since the pioneering work of Drinfeld to extend this result to the remaining types. We give a solution for the classical types B, C and D by constructing an explicit isomorphism between the R-matrix and Drinfeld presentations of the Yangian. It is based on an embedding theorem which allows us to consider the Yangian of rank \({n-1}\) as a subalgebra of the Yangian of rank n of the same type.

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Acknowledgments

We thank the support of South China University of Technology and State Administration of Foreign Experts Affairs during the work. Jing acknowledges the National Natural Science Foundation of China grant no. 11531004 and Simons Foundation grant no. 523868, Liu acknowledges the National Natural Science Foundation of China grant nos. 11531004 and 11701182, and Molev acknowledges the support of Australian Research Council.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

  2. School of Mathematics, South China University of Technology, Guangzhou, 510640, Guangdong, China

    Naihuan Jing & Ming Liu

  3. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    Alexander Molev

Authors
  1. Naihuan Jing
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  2. Ming Liu
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  3. Alexander Molev
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Correspondence to Ming Liu.

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Communicated by H. T. Yau

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Jing, N., Liu, M. & Molev, A. Isomorphism Between the R-Matrix and Drinfeld Presentations of Yangian in Types B, C and D. Commun. Math. Phys. 361, 827–872 (2018). https://doi.org/10.1007/s00220-018-3185-x

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