BEJ230 10.3150/09-BEJ230 BEJ0809-008 35 Group Representations and High-Resolution Central Limit Theorems Domenico Marinucci Dipartimento di Matematica, Universita' di Roma Tor Vergata marinucc@mat.uniroma2.it Giovanni Peccati Laboratoire de Statistique Theorique et Applique', Universite' Paris VI giovanni.peccati@gmail.com http://www.e-publications.org/ims/submission/index.php/BEJ/user/submissionFile/3890?confirm=a74dfda9