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arXiv · 1312.2771

Exotic cluster structures on $SL_{5}$

Idan Eisner
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Abstract

A conjecture by Gekhtman, Shapiro and Vainshtein suggests a correspondence between the Belavin - Drinfeld classification of solutions of the classical Yang - Baxter equation and cluster structures on simple Lie groups. This paper confirms the conjecture for $SL_{5}$. Given a Belavin - Drinfeld class, we construct the corresponding cluster structure in $\mathcal{O}\left(SL_{5}\right)$, and show that it satisfies all parts of the conjecture.

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Idan Eisner. 2013-12-10. Exotic cluster structures on $SL_{5}$. https://doi.org/10.1088/1751-8113/47/47/474002

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