Real homogenous spaces, Galois cohomology, and Reeder puzzles

摘要

Let G be a simply connected absolutely simple algebraic group defined overthe field of real numbers R. Let H be a simply connected semisimple R-subgroupof G. We consider the homogeneous space X=G/H. We ask: How many connectedcomponents has X(R)? We give a method of answering this question. Our method is based on oursolutions of generalized Reeder puzzles.