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2017 Fiscal Year Final Research Report

Research on the geometric representation theory using algebraic analysis

Research Project

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Project/Area Number 15K04790
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionOsaka 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) 兼田 正治  大阪市立大学, 大学院理学研究科, 教授 (60204575)
Project Period (FY) 2015-04-01 – 2018-03-31
Keywords代数解析 / 代数群 / 量子群 / 表現
Outline of Final Research Achievements

I obtained several results concerning the representation theory of quantum groups at roots of 1. The most important aim was to establish the Beilinson-Bernstein type correspondence for quantum groups at roots of 1. The problem is not yet solved in its full generality, but I have established it for the quantum groups of type A. This is a big progress. In connection with the quantum groups at even roots of 1, I also considered the quantum groups at q=-1 and proved that it is isomorphic to the enveloping algebra of a Lie multi-super algebra. I investigated also the quantized coordinate algebras and affine Hecke algebras, but obtained no remarkable results on them.

Free Research Field

代数群と量子群の表現論

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Published: 2019-03-29  

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