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
[Une remarque sur les représentations admissibles de niveau limite]

Présenté par : 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.

Résumé
Abstract

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 $ϑ_{11} (τ, z)$ .

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 $ϑ_{11} (τ, z)$ .

Reçu le : 2017-01-16
Accepté le : 2017-01-17
Publié le : 2017-02-01

DOI : 10.1016/j.crma.2017.01.008

Affiliations des auteurs :

Victor G. Kac ¹ ; Minoru Wakimoto ¹

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

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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/

Bibliographie
Cité par

[1] C. Beem; M. Lemos; P. Liendo; W. Peelaers; L. Rastelli; B.C. van Rees Infinite chiral symmetry in four dimensions, Commun. Math. Phys., Volume 336 (2015) no. 3, pp. 1359-1433

[2] M. Gorelik; V.G. Kac Characters of (relatively) integrable modules over affine Lie superalgebras, Jpn. J. Math., Volume 10 (2015) no. 2, pp. 135-235

[3] V.G. Kac Infinite-Dimensional Lie Algebras, Cambridge University Press, 1990

[4] V.G. Kac; S.-S. Roan; M. Wakimoto Quantum reduction of affine superalgebras, Commun. Math. Phys., Volume 241 (2003), pp. 307-342

[5] V.G. Kac; M. Wakimoto Modular invariant representations of infinite-dimensional Lie algebras and superalgebras, Proc. Natl. Acad. Sci. USA, Volume 85 (1988), pp. 4956-4960

[6] V.G. Kac; M. Wakimoto Classification of modular invariant representations of affine algebras, Advanced Series in Mathematical Physics, vol. 7, World Scientific, 1989, pp. 138-177

[7] V.G. Kac; M. Wakimoto Representations of affine superalgebras and mock theta functions, Transform. Groups, Volume 19 (2014), pp. 387-455

[8] J. Song, D. Xie, W. Yan, Chiral algebra, Higgs branch and superconformal index of the generalized Argyres–Douglas theory, in preparation.

[9] E. Verlinde Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B, Volume 300 (1988), pp. 360-375

[10] D. Xie; W. Yan; S.-T. Yau Chiral algebra of Argyres–Douglas theory from M5 brane | arXiv

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