## View abstract

### Session S16 - Quantum symmetries

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

## Charge Conserving Yang-Baxter Operators

### Eric Rowell

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.