Let G be a simply connected absolutely simple algebraic group defined over the field of real numbers R. Let H be a simply connected semisimple R-subgroup of G. We consider the homogeneous space X=G/H. We ask: how many connected components has X(R)? We give a method of answering this question. Our method is based on our solutions of generalized Reeder puzzles.
- Labelings of a Dynkin diagram
- Real Galois cohomology
- Real homogeneous space
- Reeder puzzle
- Simply connected real group