dorsal/arxiv
View SchemaSome automorphisms of Generalized Kac-Moody algebras
| Authors | J"urgen Fuchs, Urmie Ray, Christoph Schweigert |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605046 |
| URL | https://arxiv.org/abs/q-alg/9605046 |
| Journal | J.Algebra 191 (1997) 518-540 |
Abstract
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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"abstract": "To any symmetry of the Cartan matrix of a Generalized Kac-Moody (GKM) algebra\nwe associate a family of automorphisms of the algebra which act in a natural\nway on the modules of the GKM algebra. We introduce the twining character of a\nmodule which is obtained by inserting the action of such an automorphism into\nthe trace that appears in the ordinary character. Twining characters of\nintegrable highest weight modules and Verma modules satisfy a character formula\nwhich involves a certain subgroup of the Weyl group. This subgroup is shown to\nbe the Weyl group of another GKM algebra, called the orbit Lie algebra, and\nhence the twining characters coincide with ordinary characters of the orbit Lie\nalgebra.",
"arxiv_id": "q-alg/9605046",
"authors": [
"J\"urgen Fuchs",
"Urmie Ray",
"Christoph Schweigert"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"journal_ref": "J.Algebra 191 (1997) 518-540",
"title": "Some automorphisms of Generalized Kac-Moody algebras",
"url": "https://arxiv.org/abs/q-alg/9605046"
},
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