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A minimal representation of a simple non-compact Lie group is obtained by "quantizing" the minimal nilpotent coadjoint orbit of its Lie algebra. It provides context for Roger Howe's notion of a reductive dual pair encountered recently in the description of global gauge symmetry of a (4-dimensional) conformal observable algebra. We give a pedagogical introduction to these notions and point out that physicists have been using both minimal representations and dual pairs without naming them andarXiv:1006.1981v1 fatcat:ybinzdpjorel7mrtnr2hjoua3u