SL(2k,C)中两类特殊可解子群的结构及其在Fuchs系统中的应用  

Two classes of solvable subgroups of SL(2k,C) and application in Fuchsian system

作　　者：李慧珍[1] 张绍飞[2] 

机构地区：[1]装甲兵工程学院基础部数学室,北京100072 [2]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《纯粹数学与应用数学》2010年第1期164-170,共7页Pure and Applied Mathematics

基　　金：数学;信息与行为教育部重点实验室(LMIB)

摘　　要：利用SL(2,C)中可解子群的结构,给出了SL(2k,C)中两类特殊的具有两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奇点的2k阶Fuchs方程的解Riemann曲面结构,进而研究其解的大范围性质.Based on the structure of solvable subgroup in SL（2, C）, structure theorems of two classes of solvable subgroups generated by two elements in SL（2k, C） were given. By the relation between the solvability of monodromy group and the integrability of Fuchsian system, the structure of the Riemann surfaces of solutions of the 2k-order Fuchsian equation on torus with a solvable monodromy group were discussed, and some global properties of the system＇s solution were discussed.

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]