## View abstract

### 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   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloake8e40acd8b4703326294894db041eb18').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addye8e40acd8b4703326294894db041eb18 = 'r&#111;w&#101;ll' + '&#64;'; addye8e40acd8b4703326294894db041eb18 = addye8e40acd8b4703326294894db041eb18 + 'm&#97;th' + '&#46;' + 't&#97;m&#117;' + '&#46;' + '&#101;d&#117;'; var addy_texte8e40acd8b4703326294894db041eb18 = 'r&#111;w&#101;ll' + '&#64;' + 'm&#97;th' + '&#46;' + 't&#97;m&#117;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloake8e40acd8b4703326294894db041eb18').innerHTML += '<a ' + path + '\'' + prefix + ':' + addye8e40acd8b4703326294894db041eb18 + '\'>'+addy_texte8e40acd8b4703326294894db041eb18+'<\/a>';

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).