English

Exotic cluster structures on $SL_{5}$

Quantum Algebra 2015-08-14 v2 Representation Theory

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 SL5SL_{5}. Given a Belavin - Drinfeld class, we construct the corresponding cluster structure in O(SL5)\mathcal{O}\left(SL_{5}\right), and show that it satisfies all parts of the conjecture.

Cite

@article{arxiv.1312.2771,
  title  = {Exotic cluster structures on $SL_{5}$},
  author = {Idan Eisner},
  journal= {arXiv preprint arXiv:1312.2771},
  year   = {2015}
}

Comments

arXiv admin note: text overlap with arXiv:1101.0015 by other authors

R2 v1 2026-06-22T02:24:32.957Z