Real homogenous spaces, Galois cohomology, and Reeder puzzles

Abstract

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.

42 pages. The final version, to appear in J. Algebra

References in corpus (3)

• Galois cohomology of reductive algebraic groups over the field of real numbers
• Galois Cohomology of Real Groups
• Galois cohomology of real semisimple groups

Cited by in corpus (1)

• Solutions of Reeder's Puzzle