Studies of the algebraic and combinatorial structures related to quantum integrable systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 23340007
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka City University (2013-2015); Osaka University (2011-2012)
• Principal Investigator: OKADO Masato 大阪市立大学, 大学院理学研究科, 教授 (70221843)
• Co-Investigator(Kenkyū-buntansha): KUNIBA Atsuo 東京大学, 大学院総合文化研究科, 教授 (70211886) ; NAKANISHI Tomoki 名古屋大学, 多元数理科学研究科, 教授 (80227842)
• Co-Investigator(Renkei-kenkyūsha): YAMADA Yasuhiko 神戸大学, 大学院理学研究科, 教授 (00202383)
• Research Collaborator: SCHILLING Anne カリフォルニア大学デーヴィス校, 数学科, 教授
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 可積分系 / 量子群 / クラスター代数 / 組合せ論的表現論

Outline of Final Research Achievements

Principal investigator Okado constructed, with Schilling and Sakamoto, a bijection between highest weight paths and rigged configurations for type D in full generality, and thereby settled the X=M conjecture in a combinatorial way. Nakanishi studied, with his collaborators, the cluster algebra from the aspect of quantum integrable systems and clarified the periodicity, dilogarithm identities, the relation between exact WKB analysis and mutation, etc. Although it was not included in the purposes of this project in the beginning of the project period, Kuniba started the study of 3-dimensional quantum integrable systems. Later, together with Okado and other collaborators, he produced results, such as the relation between quantum coordinate rings and PBW bases, 2-dimensional reduction of the tetrahedron equation, applications to Markovian processes.

Free Research Field

数学