From Dynkin diagram symmetries to fixed point structures

Abstract

Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra induces an automorphism of the algebra and a mapping between its highest weight modules. 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'. In particular, the generating function for the trace of the map on modules, the `twining character', is equal to a character of the orbit Lie algebra. Orbit Lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory.Comment: Latex, 60 pages (extended version 63 pages), 4 uuencoded figures Formula (6.25) corrected. While this correction might be important in applications of our work, the results of the paper are not affected by it. In the present submission the "extended version" is default. In this version the corrected formula is (6.32