Some automorphisms of Generalized Kac-Moody algebras

Details Some automorphisms of Generalized Kac-Moody algebras Some automorphisms of Generalized Kac-Moody algebras

1996-05-30

arxiv.org/abs/q-alg/9605046v1

J.Algebra 191 (1997) 518-540

Physics

High Energy Physics

High Energy Physics - Theory

plain TeX, uses mssymb; 19 pages

Scientific paper

To any symmetry of the Cartan matrix of a Generalized Kac-Moody (GKM) algebra we associate a family of automorphisms of the algebra which act in a natural way on the modules of the GKM algebra. We introduce the twining character of a module which is obtained by inserting the action of such an automorphism into the trace that appears in the ordinary character. Twining characters of integrable highest weight modules and Verma modules satisfy a character formula which involves a certain subgroup of the Weyl group. This subgroup is shown to be the Weyl group of another GKM algebra, called the orbit Lie algebra, and hence the twining characters coincide with ordinary characters of the orbit Lie algebra.

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