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These are the extended notes of a mini-course given at the school WinterBraids X . We discuss algebras simultaneously related to: the braid group, the Yang–Baxter equation and the representation theory of quantum groups. The main goal is to explain the idea of the fusion procedure for the Yang–Baxter equation and to show how it leads to new examples of such algebras: the fused Hecke algebras.
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Loïc Poulain d’Andecy (2022) studied this question.
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