The relation between the configuration space and the root systems

1.(与T.T.Takayama(神户大学)合作)(3，6)型超几何函数的偏微分方程组位于射影平面上6点的位形空间上。我们处理了配置空间的两种紧化，研究了这两种紧化空间之间的关系，并构造了上述系统的局部基本解。(与吉田先生(九州大学)联合工作)Naruki的交比变换被认为是射影平面上6点的位形空间的紧致。利用这种群的性质，我们研究了实射影平面上6条直线(=6点的位形空间)的位形空间。特别地，我们用E_6.3型的根系解释了实射影平面上6条直线排列的分类。研究了实射影平面上7条直线的构型与E7型根系的关系。已知在实射影面上有11种不同的7直线排列。我从F_7.4型根系的角度对这种分类进行了解释。(与T.Fukui(Mukogawa女子大学)合作)我们研究了实射影平面上8条直线的构型与F_5型根系的关系。我们的目的是对实射影平面上8条直线排列的分类，这是一个公开问题。通过一个组合论证，我们构造了许多8行排列。

1. (Joint work with T.Takayama (Kobe Univ.)) The system of partial differential equations for the hypergeometric function of type (3,6) lives on the configuration space of 6 points on the projective plane. We treated two kinds of compactifications of the configuration space, studied the relations between these two spaces and constructed local fundamental solutions of the system above.2. (Joint work with M.Yoshida (Kyushu Univ.)) Naruki's cross ratio variety is regarded as a compactification of the configuration space of 6 points on the projective plane. Unsig the properties of this variety, we studied the configuration space of 6 lines (= the configuration space of 6 points) on the real projective plane. In particular, we gave an interpretation of the classification of 6 lines arrangements on the real projective plane in terms of the root system of type E_6.3. I studied the relationship between the configurations of 7 lines the real projective plane and the root system of type E_7. It is known that there are mutually different 11 kinds of 7 lines arrangements on the real projective plane. I gave an interpretation of the classification in terms of the root system of type F_7.4. (Joint work with T.Fukui (Mukogawa Women's Univ.)) We studied the relationship between the configurations of 8 lines the real projective plane and the root system of type F_5. Our aim is the classification of 8 lines arrangements on the real projective plane, which is an open problem. We constructed a lot of 8 lines arrangements by a combinatorial argument.