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March 2010 Periodicities of T-systems and Y-systems
Rei Inoue, Osamu Iyama, Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki
Nagoya Math. J. 197: 59-174 (March 2010). DOI: 10.1215/00277630-2009-003


The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of Yangian or quantum affine algebra associated with a complex simple Lie algebra. The unrestricted T-system admits a reduction called the restricted T-system. In this paper we formulate the periodicity conjecture for the restricted T-systems, which is the counterpart of the known and partially proved periodicity conjecture for the restricted Y-systems. Then, we partially prove the conjecture by various methods: the cluster algebra and cluster category method for the simply laced case, the determinant method for types A and C, and the direct method for types A, D, and B (level 2).


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Rei Inoue. Osamu Iyama. Atsuo Kuniba. Tomoki Nakanishi. Junji Suzuki. "Periodicities of T-systems and Y-systems." Nagoya Math. J. 197 59 - 174, March 2010.


Published: March 2010
First available in Project Euclid: 16 March 2010

zbMATH: 1250.17024
MathSciNet: MR2649278
Digital Object Identifier: 10.1215/00277630-2009-003

Rights: Copyright © 2010 Editorial Board, Nagoya Mathematical Journal


Vol.197 • March 2010
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