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Pré-Publication, Document De Travail Année : 2003

Quantum matrix algebra for the SU(n) WZNW model

P. Furlan
  • Fonction : Auteur
L. K. Hadjiivanov
  • Fonction : Auteur
A. P. Isaev
  • Fonction : Auteur
P. N. Pyatov
  • Fonction : Auteur
I. T. Todorov
  • Fonction : Auteur

Résumé

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.

Dates et versions

hal-00473329 , version 1 (15-04-2010)

Identifiants

Citer

P. Furlan, L. K. Hadjiivanov, A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov, et al.. Quantum matrix algebra for the SU(n) WZNW model. 2003. ⟨hal-00473329⟩
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