On representation theory of generalized quantum groups and algebras related to them

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400040
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: University of Toyama
• Principal Investigator: Yamane Hiroyuki 富山大学, 大学院理工学研究部(理学), 教授 (10230517)
• Co-Investigator(Renkei-kenkyūsha): YOSHII Yoji 岩手大学, 教育学部, 教授 (90462126) ; ITO Ken 愛知工業大学, 工学部, 教授 (70410587) ; OSHIMA Kazuyuki 愛知工業大学, 工学部, 准教授 (30547980)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 量子群 / スーパーリー代数 / コクセター群 / ワイル亜群 / 一般化された量子群 / 一般化されたルート系

Outline of Final Research Achievements

The article giving the classification of the finite dimensional irreducible representaions of the generalized root system was published. New proof of the Kac's list of the classification the finite dimensional irreducible representaions of the A-G type simmple Lie superalgebras was given. It was proved that any finite dimensional irreducible representaion has a highest weight vector. New and easier definition of the generalizeed root systems was given. Then it became easily seen that the root system of any A-G type simmple Lie superalgebra is a generalized root system.

Free Research Field

代数学