From Dynkin diagram symmetries to fixed point structures

J"urgen Fuchs; Bert Schellekens; Christoph Schweigert

doi:10.1007/bf02101182

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arXiv · hep-th/9506135

From Dynkin diagram symmetries to fixed point structures

J"urgen Fuchs·Bert Schellekens·Christoph Schweigert

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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.

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J"urgen Fuchs, Bert Schellekens, Christoph Schweigert. 1998-02-06. From Dynkin diagram symmetries to fixed point structures. https://doi.org/10.1007/bf02101182

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