dorsal/arxiv
View SchemaSymmetries of the Kac-Peterson Modular Matrices of Affine Algebras
| Authors | Terry Gannon |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9502004 |
| URL | https://arxiv.org/abs/q-alg/9502004 |
| DOI | 10.1007/BF01231448 |
Abstract
The characters $\chi_\mu$ of nontwisted affine algebras at fixed level define in a natural way a representation $R$ of the modular group $SL_2(Z)$. The matrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular matrices, and describe the modular behaviour of the characters. In this paper we consider all levels of $(A_{r_1}\oplus\cdots\oplus A_{r_s})^{(1)}$, and for each of these find all permutations of the highest weights which commute with the corresponding Kac-Peterson matrices. This problem is equivalent to the classification of automorphism invariants of conformal field theories, and its solution, especially considering its simplicity, is a major step toward the classification of all Wess-Zumino-Witten conformal field theories.
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"abstract": "The characters $\\chi_\\mu$ of nontwisted affine algebras at fixed level define\nin a natural way a representation $R$ of the modular group $SL_2(Z)$. The\nmatrices in the image $R(SL_2(Z))$ are called the Kac-Peterson modular\nmatrices, and describe the modular behaviour of the characters. In this paper\nwe consider all levels of $(A_{r_1}\\oplus\\cdots\\oplus A_{r_s})^{(1)}$, and for\neach of these find all permutations of the highest weights which commute with\nthe corresponding Kac-Peterson matrices. This problem is equivalent to the\nclassification of automorphism invariants of conformal field theories, and its\nsolution, especially considering its simplicity, is a major step toward the\nclassification of all Wess-Zumino-Witten conformal field theories.",
"arxiv_id": "q-alg/9502004",
"authors": [
"Terry Gannon"
],
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"q-alg",
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],
"doi": "10.1007/BF01231448",
"title": "Symmetries of the Kac-Peterson Modular Matrices of Affine Algebras",
"url": "https://arxiv.org/abs/q-alg/9502004"
},
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