Quantum matrix algebra for the SU(n) WZNW model

doi:10.1088/0305-4470/36/20/310

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Journal of Physics A: Mathematical and General

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Journal of Physics A: Mathematical and General Volume 36 Number 20 Create an alert RSS this journal

P Furlan et al 2003 J. Phys. A: Math. Gen. 36 5497 doi:10.1088/0305-4470/36/20/310

Quantum matrix algebra for the SU(n) WZNW model

P Furlan^1,2, L K Hadjiivanov^2,3, A P Isaev⁴, O V Ogievetsky^5,6, P N Pyatov⁴ and I T Todorov³

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furlan@trieste.infn.it lhadji@inrne.bas.bg isaevap@thsun1.jinr.ru oleg@cpt.univ-mrs.fr pyatov@thsun1.jinr.ru todorov@inrne.bas.bg

¹ Dipartimento di Fisica Teorica dell' Università degli Studi di Trieste, Strada Costiera 11, I-34014 Trieste, Italy
² Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Trieste, Italy
³ Theoretical Physics Division, Institute for Nuclear Research and Nuclear Energy, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria
⁴ Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141 980 Moscow Region, Russia
⁵ Centre de Physique Théorique, Luminy, F-13288 Marseille, France
⁶ On leave of absence from: P N Lebedev Physical Institute, Theoretical Department, 117924 Moscow, Leninsky prospect 53, Russia.

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Abstract References Cited By

The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra Script A generated by an n × n matrix a = (aⁱ_α), i, α = 1, ..., n (with noncommuting entries) and by rational functions of n commuting elements q^p_i satisfying ∏ⁿ_{i = 1}q^p_i = 1, q^p_ia^j_α = a^j_αq^{p_i+δ^j_i − 1/n}. We study a generalization of the Fock space ( Script F ) representation of Script 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 = U_q(sl_n), with each irreducible representation entering with multiplicity 1. For an integer hat s hat u (n) height h ( = k + n ≥ n) the complex parameter q is an even root of unity, q^h = −1, and the algebra Script A has an ideal Script I _h such that the factor algebra _h = /_h is finite dimensional. All physical U_q modules—of shifted weights satisfying p_1n ≡ p₁ − p_n < h—appear in the Fock representation of _h.