The diagram category of framed tangles and invariants of quantized symplectic group
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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.
Keywordsdiagram category of framed tangles invariant theory quantized symplectic group Birman-Murakami-Wenzl algebra
MSC(2010)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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