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Session S16 - Quantum symmetries

Monday, July 19, 20:30 ~ 20:55 UTC-3

Charge Conserving Yang-Baxter Operators

Eric Rowell

Texas A&M University, United States - rowell@math.tamu.edu

An operator $R$ on $V\otimes V$ is charge conserving if the span of $e_i\otimes e_j,e_j\otimes e_i$ is $R$ -invariant. For example, the universal $R$ -matrix associated with $U_q\mathfrak{sl}_2$ is charge conserving. We study the problem of classifying charge conserving Yang-Baxter operators in all dimensions. Using special symmetries we can give a characterization of all such $n^2\times n^2$ solutions, and discover a remarkable combinatorial relationship with hierarchical orderings on $n$ individuals.

Joint work with Paul Martin (University of Leeds).

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