SOME EXAMPLES IN THE REALIZATION OF SYMMETRY

I briefly discuss three phenomena arising in recent work where the rea lization of symmetries in quantum mechanics is unusual. The first of t hese is, I believe, the very simplest realization of non-trivial confi nement by a mechanism of charge-flux frustration. It arises in models having several coupled abelian Chern-Simons gauge symmetries, which cl osely resemble effective theories used for the quantum Hall effect. Th e second is symmetry obstruction by non-abelian flux, which has implic ations for 2+1 dimensional supergravity. Third is the possibility of n ew varieties of quantum statistics: non-abelian and projective.