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Yang-Baxter representations of the infinite symmetric group

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OASW03 - Subfactors, K-theory and conformal field theory

The Yang-Baxter equation (YBE) lies at the heart of many subjects, including quantum statistical mechanics, QFT , knot theory, braid groups, and subfactors. In this talk, I will consider involutive solutions of the YBE (“R-matrices”). Any such R-matrix defines a representation and an extremal character of the infinite symmetric group as well as a corresponding tower of subfactors. 

Using these structures, I will describe how to find all R-matrices up to a natural notion of equivalence (given by the character and the dimension), how to completely parameterize the set of solutions, and how to decide efficiently whether two given R-matrices are equivalent. Joint work with U. Pennig and S. Wood.

This talk is part of the Isaac Newton Institute Seminar Series series.

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