Minimal representations and reductive dual pairs in conformal field theory

Details Minimal representations and reductive dual pairs in conformal field theory Minimal representations and reductive dual pairs in conformal field theory

2010-06-10

arxiv.org/abs/1006.1981v1

Invited lecture at the 8th International Workshop on Lie Theory and Its Applications in Physics, Varna, June 2009; ed. V. Dobr

Physics

Mathematical Physics

21 pages

Scientific paper

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 hence stand a chance to understand their theory and to profit from it.

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