The classification of zamolodchikov periodic quivers

Pavel Galashin, Pavlo Pylyavskyy

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity are in bijection with pairs of commuting Cartan matrices of finite type. Such pairs were classified by Stembridge in his study of W-graphs. The classification includes products of Dynkin diagrams along with four other infinite families, and eight exceptional cases. We provide a proof of Zamolodchikov periodicity for all four remaining infinite families, and verify the exceptional cases using a computer program.

Original languageEnglish (US)
Pages (from-to)447-484
Number of pages38
JournalAmerican Journal of Mathematics
Volume141
Issue number2
DOIs
StatePublished - Apr 2019

Bibliographical note

Funding Information:
Manuscript received May 21, 2016. Research of the second author supported by NSF grants DMS-1148634, DMS-1351590, and Sloan Fellowship. American Journal of Mathematics 141 (2019), 447–484. ©c 2019 by Johns Hopkins University Press.

Fingerprint Dive into the research topics of 'The classification of zamolodchikov periodic quivers'. Together they form a unique fingerprint.

Cite this