QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Representations of the braid group and applications

Nikos Karaiskos

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We briefly review elements of the braid group and its role in the field of quantum integrability. After introducing particular representations of the Hecke and Temperley-Lieb algebras, we discuss the existence of a large number of non-trivial quantum symmetries for the latter one. We exploit the representations for constructing solutions to the Yang-Baxter and reflection equations and comment on possible further uses.