Algebraic analysis of difference equations arising from integrable systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400106
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Tsukuba
• Principal Investigator: TAKEYAMA Yoshihiro 筑波大学, 数理物質系, 准教授 (60375392)
• Co-Investigator(Renkei-kenkyūsha): NAGOYA Hajime 金沢大学, 数物科学系, 准教授 (80447367) ; TANAKA Tatsushi 京都産業大学, 理学部, 准教授 (60515196)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 可積分系 / 確率過程 / 多重ゼータ値 / q類似

Outline of Final Research Achievements

We studied algebraic structure of integrable stochastic systems and a q-analogue of multiple zeta values (qMZV). First, we constructed new integrable stochastic systems using a representation of a deformation of the affine Hecke algebra. Regarding the multi-spices q-Boson model, which is an integrable stochastic system constructed as above, we obtained an explicit formula for eigenfunctions of its generator. Second, we found that the finite sum obtained by setting the parameter q in qMZVs to a root of unity simultaneously produces important objects in number theory called finite/symmetrized multiple zeta values.

Free Research Field

数理物理学