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Twining character formula of Kac-Wakimoto type for affine Lie algebras


Author: Satoshi Naito
Journal: Represent. Theory 6 (2002), 70-100
MSC (2000): Primary 17B67; Secondary 17B10, 17B40
DOI: https://doi.org/10.1090/S1088-4165-02-00120-6
Published electronically: July 16, 2002
MathSciNet review: 1915087
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Abstract: We prove a formula of Kac-Wakimoto type for the twining characters of irreducible highest weight modules of symmetric, noncritical, integrally dominant highest weights over affine Lie algebras. This formula describes the twining character in terms of the subgroup of the integral Weyl group consisting of elements which commute with the Dynkin diagram automorphism. The main tools in our proof are the (Jantzen) translation functor and the existence result of a certain local composition series which is stable under the Dynkin diagram automorphism.


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Additional Information

Satoshi Naito
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Email: naito@math.tsukuba.ac.jp

DOI: https://doi.org/10.1090/S1088-4165-02-00120-6
Keywords: Affine Lie algebra, character, diagram automorphism
Received by editor(s): December 19, 2000
Received by editor(s) in revised form: February 17, 2002
Published electronically: July 16, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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