A remark on boundary level admissible representations

Victor G. Kac; Minoru Wakimoto

doi:10.1016/j.crma.2017.01.008

Lie algebras

A remark on boundary level admissible representations

Presented by: Michèle Vergne

Victor G. Kac ¹; Minoru Wakimoto ¹

¹ Department of Mathematics, M.I.T., Cambridge, MA 02139, USA

Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 128-132.

Abstract
Résumé

We point out that it is immediate by our character formula that in the case of a boundary level the characters of admissible representations of affine Kac–Moody algebras and the corresponding W-algebras decompose in products in terms of the Jacobi form $ϑ_{11} (τ, z)$ .

Nous remarquons la conséquence suivante de notre formule de caractères. Pour un niveau limite, les caractères d'une représentation admissible d'une algèbre de Kac–Moody affine ainsi que de la W-algèbre correspondante s'expriment comme des produits de formes de Jacobi $ϑ_{11} (τ, z)$ .

Received: 2017-01-16
Accepted: 2017-01-17
Published online: 2017-02-01

DOI: 10.1016/j.crma.2017.01.008

Author's affiliations:

Victor G. Kac ¹; Minoru Wakimoto ¹

¹ Department of Mathematics, M.I.T., Cambridge, MA 02139, USA

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     title = {A remark on boundary level admissible representations},
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Victor G. Kac; Minoru Wakimoto. A remark on boundary level admissible representations. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 128-132. doi : 10.1016/j.crma.2017.01.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.008/

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