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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Twining Character Formula of Kac-Wakimoto Type for Affine Lie Algebras
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by Satoshi Naito PDF
Represent. Theory 6 (2002), 70-100 Request permission


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:
  • Received by editor(s): December 19, 2000
  • Received by editor(s) in revised form: February 17, 2002
  • Published electronically: July 16, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Represent. Theory 6 (2002), 70-100
  • MSC (2000): Primary 17B67; Secondary 17B10, 17B40
  • DOI:
  • MathSciNet review: 1915087