Deformation of Lie subalgebras and systems of hypergeometric equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540002
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: SAITO Mutsumi 北海道大学, 理学(系)研究科(研究院), 教授 (70215565)
• Co-Investigator(Renkei-kenkyūsha): YAMASHITA Hiroshi 北海道大学, 大学院理学研究院, 教授 (30192793) ; ABE Noriyuki 北海道大学, 大学院理学研究院, 准教授 (00553629) ; OKUYAMA Go 北海道科学大学, 保健医療学部, 准教授 (60433421)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: カルタン部分リー代数の変形 / 可換部分リー代数 / グラスマン多様体

Outline of Final Research Achievements

Related to confluence of the systems of hypergeometric equations a la Gelfand, deformation of Cartan subalgebras is studied. Let g be a complex simple Lie algebra of rank n. We have proved that an n-dimensional ideal of a Borel subalgebra is a limit of Jordan Lie subalgebras, which is the centralizer of a regular nilpotent element. Since a Jordan Lie subalgebra is a limit of Cartan subalgebras, an n-dimensional ideal of a Borel subalgebra is also a limit of Cartan subalgebras.
Furthermore, combining with a classical result due to Kostant, we see that the g-module composed of all n-dimensional abelian subalgebras is spanned by Cartan subalgebras or Jordan Lie subalgebras.

Free Research Field

代数学