SL(n,C)上一类特殊可解子群的结构及其在Fuchs系统中的应用  

Structure of Solvable Subgroups in SL(n,C) and Its Application to Fuchsian System

作　　者：朱秀丽[1] 张绍飞[2] 邱菀华[1] 

机构地区：[1]北京航空航天大学经管学院,北京100083 [2]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《大学数学》2011年第1期52-55,共4页College Mathematics

摘　　要：给出了SL(n,C)中一类特殊的具有有限个生成元的可解子群的结构定理.由单值群的可解性与Fuchs系统的可积性之间的关系,研究对应的单值群是可解的环面上只有一个正则起点的n阶Fuchs方程的解Riemann曲面结构,进而研究其解的大范围性质.It is given a structure of solvable subgroup which has finite element in this paper.The solvable group of SL（n,C） and the solvability of Fuchsian equation are contracted by Khovanskiy theorem,such that the solvability of Fuchsian equation＇ research is transformed the solvability of its monodromy group＇ research.On the basis of the structure theorem of solvable group in SL（n,C）,we will discuss the structure of solvable group in SL（n,C）,and we will apply it to the study of the integrability of Fuchsian equation.

关 键 词：Fuchs系统 单值群 特殊线性群 可解群 可积性 

分 类 号：O152[理学—数学]