On involutive solutions to the quantum Yang-Baxter equation (yielding representations of symmetric groups):
Gandalf Lechner, Ulrich Pennig, Simon Wood: Yang-Baxter representations of the infinite symmetric group, Adv. Math., Vol. 355 (2019) 106769 [arXiv:1707.00196, doi:10.1016/j.aim.2019.106769]
Gandalf Lechner: All involutive solutions of the Yang-Baxter equation, talk at Advances in Mathematics and Theoretical Physics (2017) [pdf, pdf]
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