In this talk, I will describe some general constraints on the existence
of many-body localized (MBL) phases in the presence of global
symmetries. Based only on representation theory, I will derive some
general Mermin-Wagner-type principles governing the possible fates of
non-equilibrium dynamics in isolated, disordered quantum systems. In
particular, I will show that MBL cannot exist in the presence of
non-Abelian symmetries. Consequences for the classification of MBL
protected topological phases (and Floquet phases) will be discussed.
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