I briefly discuss three phenomena arising in recent work where the
realization of symmetries in quantum mechanics is unusual. The first of these
is, I believe, the very simplest realization of non-trivial confinement by a
mechanism of charge-flux frustration. It arises in models having several
coupled abelian Chern-Simons gauge symmetries, which closely resemble effective
theories used for the quantum Hall effect. The second is symmetry obstruction
by non-abelian flux, which has implications for 2+1 dimensional supergravity.
Third is the possibility of new varieties of quantum statistics: non-abelian
and projective.Comment: LaTeX, 7 Page
