The diagram category of framed tangles and invariants of quantized symplectic group

  • Zhankui XiaoEmail author
  • Yuping Yang
  • Yinhuo Zhang


In this paper, we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups. Our methods depend on the theory of braided strict monoidal categories which are pivotal, more explicitly, the diagram category of framed tangles.


diagram category of framed tangles invariant theory quantized symplectic group Birman-Murakami-Wenzl algebra 


17B37 18D10 20G05 16T30 


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The first author was supported by the National Natural Science Foundation of China (Grant No. 11301195), China Scholarship Council and a research foundation of Huaqiao University (Grant No. 2014KJTD14). The work was done while the first author was visiting the University of Hasselt and he is very grateful for its hospitality. The authors thank the referees for their valuable comments and suggestions.


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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesHuaqiao UniversityQuanzhouChina
  2. 2.Department of Mathematics & StatisticsUniversity of Hasselt, Universitaire CampusDiepeenbeekBelgium

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