Algebraic analysis of infinite symmetry

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340005
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: KASHIWARA Masaki 京都大学, 数理解析研究所, 研究員 (60027381)
• Co-Investigator(Renkei-kenkyūsha): ARIKI Susumu 大阪大学, 大学院情報科学研究科, 教授 (40212641) ; TANISAKI Toshiyuki 大阪市立大学, 理学研究科, 教授 (70142916) ; NAKASHIMA Toshiki 上智大学, 理工学部, 教授 (60243193) ; KATO Syu 京都大学, 理学部, 准教授 (40456760) ; MIWA Tetsuji 京都大学, 国際高等教育院, 特定教授 (10027386)
• Research Collaborator: SCHAPIRA Pierre ; KANG Seok-Jin ; VILONEN Kari ; D'AGNOLO Andrea
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 表現論 / リーマン・ヒルベルト対応 / 圏化

Outline of Final Research Achievements

There are three significant results of the research on representation theory during these five years.
First, I proved the Riemann-Hilbert correspondence for holonomic D-modules (with A. D'Agnolo). Second, I proved ``codimension-three conjecture''(with K. Vilonen). Third, I established a categorification of quantum groups via cyclotomic quiver Hecke algebras (with S-J. Kang).

Free Research Field

数学