Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups

Abstract

We prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group. We give the formula for the corresponding multiplicities in the case of the quotient quantum spaces. We describe the subgroups and the quotient spaces of quantum SU(2) and SO(3) groups.