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What are some mathematical applications of Quantum Groups?

I have tried researching and found that it is used to find solutions to Yang-Baxter equation.

Any other applications?

Thanks a lot.

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    In the framework of algebraic geometry, representation theory and mathematical physics$a$interesting topic, this associate with quantum cohomology. This recent work http://arxiv.org/abs/1211.1287 can explain this well.2014-09-03

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