Minimal orbits of the isotropy groups of symmetric spaces of compact type

✍ Scribed by Daigo Hirohashi; Hiroyuki Tasaki; Hyunjung Song; Ryoichi Takagi

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 75 KB
• Volume: 13
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00022-x

✦ Synopsis

Let M be a compact symmetric space, and K the isotropy subgroup of the group of all isometries of M at a point o of M. We consider two actions of K , namely the natural action of K on M and the linear isotropy action of K on the tangent space T o M. In both cases, we show that in each category of orbits of the "same type" under K there exists a unique minimal one.