FROM DYNKIN DIAGRAM SYMMETRIES TO FIXED-POINT STRUCTURES

Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody al gebra g induces an automorphism of g and a mapping tau(omega) between highest weight modules of g. For a large class of such Dynkin diagram automorphisms, we can describe various aspects of these maps in terms of another Kac-Moody algebra, the ''orbit Lie algebra'' g. In particul ar, the generating function for the trace of tau(omega) over weight sp aces, which we call the ''twining character'' of g (with respect to th e automorphism), is equal to a character of g. The orbit Lie algebras of untwisted affine Lie algebras turn out to be closely related to the fixed point theories that have been introduced in conformal field the ory. Orbit Lie algebras and twining characters constitute a crucial st ep towards solving the fixed point resolution problem in conformal fie ld theory.