Periodicity of Y-systems

introduction

• periodicity (Keller) \[Y_{\mathbf{i}}(u+2(h+h'))=Y_{\mathbf{i}}(u)\]
• half-periodicity \[Y_{\mathbf{i}}(u+(h+h'))=Y_{\sigma(\mathbf{i})}(u)\] where \(\sigma\) is the involution of the pair of Dynkin diagram

expositions

• Volkov, 2010 Periodicity conjecture for Y-systems
• Keller, Bernhard. 2008. “Cluster Algebras, Quiver Representations and Triangulated Categories”. ArXiv e-print 0807.1960. http://arxiv.org/abs/0807.1960.

articles

• Pavel Galashin, Pavlo Pylyavskyy, The classification of Zamolodchikov periodic quivers, http://arxiv.org/abs/1603.03942v1
• Daping Weng, Donaldson-Thomas Transformation of Grassmannian, http://arxiv.org/abs/1603.00972v1
• Pylyavskyy, Pavlo. “Zamolodchikov Integrability via Rings of Invariants.” arXiv:1506.05378 [math], June 17, 2015. http://arxiv.org/abs/1506.05378.
• Kase, Ryoichi. “Remarks on Lengths of Maximal Green Sequences for Quivers of Type \(\tilde{A}_{n,1}\).” arXiv:1507.02852 [math], July 10, 2015. http://arxiv.org/abs/1507.02852.
• Muller, Greg. “The Existence of a Maximal Green Sequence Is Not Invariant under Quiver Mutation.” arXiv:1503.04675 [math], March 16, 2015. http://arxiv.org/abs/1503.04675.