Extension of special functions from the viewpoint of integrable systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540252
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Rikkyo University
• Principal Investigator: KAKEI Saburo 立教大学, 理学部, 教授 (60318798)
• Co-Investigator(Renkei-kenkyūsha): SAITO Yoshihisa 東京大学, 数理科学研究科, 准教授 (20294522) ; WILLOX Ralph 東京大学, 数理科学研究科, 教授 (20361610)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 可積分系

Outline of Final Research Achievements

This research project aims to extend the theory of integrable systems and special functions. We have focused mainly on applications to differential geometry and combinatorics, and obtained the following results;
(1) Goldstein and Petrich introduced a hierarchy of equations that governs isoperimetric deformation of plane curves. We have revealed that the Goldstein-Petrich hierarchy is indeed a reduced case of the Toda lattice hierarchy. (2) We have studied rigged configurations from the viewpoint of soliton cellular automaton. We have obtained alternative proof of the linearization property of the time-evolution, which is simpler than the known proofs.
We have obtained still other preliminary results that are related to applications of integrable systems to differential geometry and combinatorics. We will investigate them further in near future.

Free Research Field

数理物理学