Studies on quantum integrable systems and multiple zeta functions

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Rikkyo University
• Principal Investigator: KOMORI Yasushi 立教大学, 理学部, 准教授 (80343200)
• Co-Investigator(Renkei-kenkyūsha): MATSUMOTO Kohji 名古屋大学, 多元数理科学研究科, 教授 (60192754) ; TSUMURA Hirofumi 首都大学東京, 理工学研究科, 教授 (20310419)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 量子可積分系 / 多重ゼータ関数

Outline of Final Research Achievements

Both partition functions in quantum gauge theories and zeta-functions in mathematics, which play fundamental and important roles in each area, happen to coincide in some cases. Among them are the Witten zeta-functions. These zeta-functions are the main objects and should be studied from various viewpoints. For this problem, we proposed lattice sums associated with hyperplane arrangements and established a unified way to treat these values and functional relations among Witten zeta-functions via their generating functions. We also studied some properties of related zeta-functions and hypergeometric functions, and obtained new functional relations and formulas.

Free Research Field

数物系科学