Periodicities of T-systems and Y-systems, Dilogarithm Identities, and Cluster Algebras II: Types Cr, F4, and G2

被引：22

作者：

Inoue, Rei ^{[1
]}

Iyama, Osamu ^{[2
]}

Keller, Bernhard ^{[3
]}

Kuniba, Atsuo ^{[4
]}

Nakanishi, Tomoki ^{[2
]}

机构：

[1] Suzuka Univ Med Sci, Fac Pharmaceut Sci, Suzuka 5138670, Japan

[2] Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648604, Japan

[3] Univ Paris 07, Inst Math Jussieu, CNRS, UFR Math,UMR 7586, F-75251 Paris 05, France

[4] Univ Tokyo, Inst Phys, Tokyo 1538902, Japan

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 2013年 / 49卷 / 01期

关键词：

T-systems; Y-systems; cluster algebra; dilogarithm;

D O I：

10.4171/PRIMS/96

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the periodicities of the restricted T-systems and Y-systems associated with the quantum affine algebra of type C-r, F-4, and G(2) at any level. We also prove the dilogarithm identities for these Y-systems at any level. Our proof is based on the tropical Y-systems and the categorification of the cluster algebra associated with any skew-symmetric matrix by Plamondon.

引用

页码：43 / 85

页数：43

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