Abstract
We introduce a new family of examples of ‘quantum groups’. Its irreducible representations are indexed by level l dominant integral weights of affine Lie algebra sī(n), and their branching rules with respect to the ‘truncated tensor product’ \(\bar\otimes \) is given by the fusion rules of SU(n) l -Wess-Zumino-Witten model in conformal field theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abe, A., Hopf Algebras, Cambridge Tracts in Math. 74, Cambridge University Press, 1980.
Drin'feld, V., Quantum groups, Proc. ICM, Berkeley, 1968, pp. 798–820.
GepnerD. and WittenE., String theory on group manifolds, Nuclear Phys. B 278, 493–549 (1986).
GoodmanF. and NakanishiT., Fusion algebras in integrable systems in two dimensions, Phys. Lett. B 262, 259–264 (1991).
GoodmanF. and WenzlH., Littlewood-Richardson coefficients for Hecke algebras at roots of unity, Adv. in Math. 82, 244–265 (1990).
Hayashi, T., in preparation.
JimboM., Quantum R matrix related to the generalized Toda system: an algebraic approach, Lecture Notes in Phys. 246, Springer, Berlin, 1986, pp. 335–361.
JimboM., KunibaA., MiwaT., and OkadoM., The Ainfn/sup(1) face models, Comm. Math. Phys. 119, 543–565 (1988).
JimboM., MiwaT. and OkadoM., Solvable lattice models whose states are dominant integral weight of Ainfn−1/sup(1). Lett. Math. Phys. 14, 123–131 (1987).
Kac, V., Infinite Dimensional Lie Algebras, 3rd edn., Cambridge Univ. Press, 1990.
KniznikV. and ZamolodchikovA., Current algebra and Wess-Zumino models in two dimensions, Nuclear Phys. B 247, 83–103 (1984).
KulishP., ReshetikhinN., and SklyaninE., Yang-Baxter equation and representation theory. I, Lett. Math. Phys. 5, 393–403 (1981).
TsuchiyaA. and KanieY., Vertex operators in conformal field theory on 296-1 and monodromy representations of braid groups, Adv. Stud. Pure Math. 16, 297–372 (1988).
VerlindeE., Fusion rules and modular transformations in 2D conformal field theory, Nuclear Phys. B 300, 360–376 (1988).
WaltonM., Algorithm for the WZW fusion rules: a proof, Phys. Lett. B 241, 365–368 (1990).
WoronowiczS., Tannaka-Klein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93, 35–76 (1988).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hayashi, T. An algebra related to the fusion rules of Wess-Zumino-Witten models. Lett Math Phys 22, 291–296 (1991). https://doi.org/10.1007/BF00405604
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00405604