Minimal representations and reductive dual pairs in conformal field theory [article]

Ivan Todorov
2010 arXiv   pre-print
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 and
more » ... e stand a chance to understand their theory and to profit from it.
arXiv:1006.1981v1 fatcat:ybinzdpjorel7mrtnr2hjoua3u