Research on the representation theory of algebraic groups using algebraic analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka City University
• Principal Investigator: TANISAKI Toshiyuki 大阪市立大学, 大学院理学研究科, 教授 (70142916)
• Co-Investigator(Kenkyū-buntansha): KANEDA Masaharu 大阪市立大学, 大学院理学研究科, 教授 (60204557)
• Co-Investigator(Renkei-kenkyūsha): SAITO Yoshihisa 東京大学, 大学院数理科学研究科, 准教授 (20294522)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 代数解析 / 代数群 / 表現

Outline of Final Research Achievements

We completely determined the structure of the center of a quantized enveloping algebra at an odd root of unity. This gives the variety consisting of central characters. In order to develop the representation theory we need more information about the Poisson structure of this variety. We have almost accomplished it although there remain some points to be checked. We also investigated the representation theory of quantized coordinate algebras. In particular, we have given a description of the Soibelman module via generators and relations. Using this we gave a unified proof of a result of Kuniba-Okado-Yamada. Moreover, we gave a proof of their conjecture. We investigated the Drinfeld pairing of the quantized enveloping algebra by algebraic methods. We gave a new simpler proof of the fact that the Drinfeld pairing is invariant under the action of the braid group.

Free Research Field

代数群の表現論