Tensor products and fusion rules

M. A. Walton

doi:10.1139/p94-067

Tensor products and fusion rules

Canadian Journal of Physics ◽

10.1139/p94-067 ◽

1994 ◽

Vol 72 (7-8) ◽

pp. 527-536 ◽

Cited By ~ 6

Author(s):

M. A. Walton

Keyword(s):

Lie Algebras ◽

Tensor Products ◽

Fusion Rules ◽

Semisimple Lie Algebras

Methods of decomposing tensor products of integrable representations of semisimple Lie algebras are described. They include a formula due to Zelobenko, the descendant of a conjecture made by Parthasarathy et al., and identities found by Feingold. The methods are adapted to the calculation of fusion rules in Wess–Zumino–Novikov–Witten models.

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A generalization of the alcove model and its applications

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3090 ◽

2012 ◽

Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽

Author(s):

Cristian Lenart ◽

Arthur Lubovsky

Keyword(s):

Lie Algebras ◽

Energy Function ◽

Tensor Products ◽

Present Evidence ◽

Semisimple Lie Algebras ◽

Highest Weight ◽

International Audience ◽

Alcove Model

International audience The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. We prove the conjecture in types $A$ and $C$. We also present evidence for the fact that a related statistic computes the energy function. Le modèle des alcôves du premier auteur et Postnikov décrit les cristaux de plus haut poids des algèbres de Lie semi-simples. Nous présentons une généralisation, appelée le modèle des alcôves quantique, et nous conjecturons qu’il décrit dans une manière uniforme les produits tensoriels des cristaux de Kirillov-Reshetikhin de type colonne, pour toutes les types affines symétriques. Nous prouvons la conjecture dans les types $A$ et $C$. Nous fournissons aussi des preuves qu’une statistique associée donne la fonction d’énergie.

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NEW EXCEPTIONAL $(A_1^{(1)})^{\oplus r} $ INVARIANTS AND THE ASSOCIATED GEPNER MODELS

International Journal of Modern Physics A ◽

10.1142/s0217751x92001009 ◽

1992 ◽

Vol 07 (10) ◽

pp. 2245-2264 ◽

Cited By ~ 7

Author(s):

JÜRGEN FUCHS ◽

ALBRECHT KLEMM ◽

MICHAEL G. SCHMIDT ◽

DIRK VERSTEGEN

Keyword(s):

Lie Algebras ◽

Infinite Series ◽

Tensor Products ◽

Heterotic String ◽

Partition Functions ◽

Affine Lie Algebras ◽

Affine Algebra ◽

Modular Invariant ◽

Fusion Rules ◽

Modular Invariants

New modular invariant partition functions for tensor products of [Formula: see text] affine Lie algebras are presented. These exceptional modular invariants can be understood in terms of automorphisms of the fusion rules of the affine algebra or of its extensions. There are three isolated cases, as well as an infinite series of new invariants. As an application, the new modular invariants are employed to produce new Gepner type compactifications of the heterotic string.

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WZW fusion rules for the classical Lie algebras

Canadian Journal of Physics ◽

10.1139/p94-050 ◽

1994 ◽

Vol 72 (7-8) ◽

pp. 342-344 ◽

Cited By ~ 1

Author(s):

C. J. Cummins ◽

R. C. King

Keyword(s):

Lie Algebras ◽

Young Diagram ◽

Tensor Products ◽

Fusion Rules

Fusion rules for WZW models based on the Lie algebras su(n), sp(2n) and so(n) are considered. Previous work has shown how, in the cases of su(n) and sp(2n), fusion rules may be computed using Young diagram methods and applying fusion modification rules similar to the rank modification rules required for tensor products. In this note we extend these results to include the so(n) case.

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