Nakanishi Tomoki

Publications (2)0 Total impact

• Source

  Available from: ArXiv

  Article: Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems

  Nakanishi Tomoki, Tateo Roberto
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  ABSTRACT: We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been conjectured earlier. In particular, this provides new examples of periodicities of seeds.
  Symmetry, Integrability and Geometry : Methods and Applications. 01/2010;
• Source

  Available from: Atsuo Kuniba

  Article: T-Systems and Y-Systems for Quantum Affinizations of Quantum Kac-Moody Algebras

  Kuniba Atsuo, Nakanishi Tomoki, Suzuki Junji
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  ABSTRACT: The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras by Hernandez. In this note we introduce the corresponding Y-systems and establish a relation between T and Y-systems. We also introduce the T and Y-systems associated with a class of cluster algebras, which include the former T and Y-systems of simply laced type as special cases.
  Symmetry, Integrability and Geometry: Methods and Applications. 01/2009;