MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

Here they study Markov chains on $G/H$ using that the endomorphism algebra is commutative. Specific examples coming from symmetric groups and wreath products can be found in the book. Also Weilandt's classical book on permutation groups has a chapter on centralizer algebras and the connection with orbitals is made clear.