An application of global analysis of differential equations to representation theory

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800072
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Josai University
• Principal Investigator: Hiroe Kazuki 城西大学, 理学部, 助教 (50648300)
• Research Collaborator: OSHIMA Toshio 城西大学, 理学部数学科, 教授 (50011721) ; YAMAKAWA Daisuke 東京理科大学, 理学部第一部数学科, 講師 (20595847)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 不確定特異点 / ワイル群 / ミドル・コンボリューション / 箙の表現論

Outline of Final Research Achievements

I gave an isomorphism between a moduli space of algebraic differential equations on the Riemann sphere and　quiver variety as symplectic manifolds when differential equations have at most one unramified　irregular singular point. When the differential equations have arbitrary number of unramified irregular singular　points, although it was known that the moduli space can not be isomorphic to any quiver varieties, I constructed　an open embedding into a quiver variety which is not surjective in general and clarified a　relation between middle convolution of differential equations and Wely group of the quiver, also determined a　necessary and sufficient conditon to the nonemptiness of the regular part of the moduli space.

Free Research Field

微分方程式の不確定特異点論