Twining Character Formula of Kac-Wakimoto Type for Affine Lie Algebras

Naito, Satoshi

doi:10.1090/S1088-4165-02-00120-6

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

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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Character formula of Kac-Wakimoto type for generalized Kac-Moody algebras

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