方型锥上第一类Siegel域

<正> 记V为R~n中不包含直线的仿射齐性开凸锥(简称齐性锥),则C~n中点集■(V)={z∈C~n|Im(z)∈V}称为齐性锥V上第一类Siegel域,它仿射齐性.熟知齐性锥V上第一类Siegel域在解析等价下的分类即齐性锥在仿射等价下的分类.这方面已有结果为Vinberg关于仿射齐性自共轭锥的分类. 本文考虑方型锥,即这种齐性锥,它仿射等价于适合条件

THE FIRST KIND SIEGEL DOMAINS OVER THE CONES WITH SQUARE TYPE

In the papers 2] and 3], we defined the N- type homogeneous cones, denoted by V_N. We proved that any affine homogeneous cone was affine equivalent to the Ntype homogeneous cone. In this paper, we restricted the cone V_N by the condition n_(1j)=n_(2j)=…n_(j-1,j)=σ_j≠0, 2≤j≤N, and denoted V_N by V(σ_2,…, σ_N). The cone V(σ_2, …, σ_N) is called the square cone.In §1, we solved the classification of the first kind of siegel domain over square cones. These canonical domains are N=1, (V_1); N=2, (V(σ_2)); N=3, Using2],we also determinated the full analytic homeomorphism group for the canonical domains in §2. In §3, independent to 1], we gave a new proof of classification of affine homogeneous self-conjugate cones, and proved that these cones are the topological product of the square cones V_1, V(σ_2), V(8, 8), V(1,…, 1), V(2,…, 2), V(4, …, 4). Therefore the result of classification of affine homogeneous self-conjugate cones is also obtained.