Exotic cluster structures on SL5

A conjecture by Gekhtman, Shapiro and Vainshtein suggests a correspondence between the Belavin–Drinfeld (BD) classification of solutions of the classical Yang–Baxter equation and cluster structures on simple Lie groups. This paper confirms the conjecture for SL5. Given a BD class, we construct the corresponding cluster structure in O(SL5), and show that it satisfies all parts of the conjecture. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Cluster algebras in mathematical physics'. (paper)