Pursuit of analogies between quantum difference isomonodromic systems, quantum Teichmuller theory, and solvable lattice models

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400033
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: Hasegawa Koji 東北大学, 理学研究科, 准教授 (30208483)
• Co-Investigator(Renkei-kenkyūsha): Yamada Yasuhiko 神戸大学, 大学院理学研究科, 教授 (00202383) ; Kuroki Gen 東北大学, 大学院理学研究科, 助教 (10234593)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 量子群 / パンルヴェ方程式 / 可積分系

Outline of Final Research Achievements

This project is to pursuit the analogies between the quantum isomonodromic systems, quantum Teichmuller theory, and the solvable statistical lattice models in two dimension. It involves many structures nd aspects such as symmetries in quantum discrete Garnier systems and quantized tau function, as well as quantization of the so-called confluent procedure from the viewpoint of lattice models, and the quantized Teichmuller theory as the geometric counterpart of the solvable lattice theory. For all of these theme the proper understanding for the quantum discrete La x matrix is important. We have explored some of the relevant structures e.g. the appropriate root ordering problem in the formula of universal R matrix to obtain the appropriate Lax matrices. Still there are remaining problems, one of the main issue is to understand the infinitely many poles arising from the imaginary root factors in a proper way.

Free Research Field

数学