Quantum matrix algebra for the SU(n) WZNW model

Abstract

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_α) (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.

48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys. A

References in corpus (19)

• A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
• Lattice Wess-Zumino-Witten Model and Quantum Groups
• The many faces of Ocneanu cells
• Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids
• Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras
• Characteristic Relations for Quantum Matrices
• Operator realization of the SU(2) WZNW model
• Quadratic brackets from symplectic forms
• Twisted Yang-Baxter equations for linear quantum (super)groups
• Quantisation of the SU(N) WZW Model at Level $k$
• Representation Theory of Lattice Current Algebras
• The Chiral WZNW Phase Space and its Poisson-Lie Groupoid
• Chiral Quantization of the WZW $SU(n)$ Model
• A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model
• (T*B)_q, q-analogue of model space and CGC generating matrices
• Monodromy Representations of the Braid Group
• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Vertex Operators - From a Toy Model to Lattice Algebras
• Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners

Cited by in corpus (6)

• Spectral extension of the quantum group cotangent bundle
• Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model
• Quantum su(n)_k monodromy matrices
• Differential Calculus on h-Deformed Spaces
• Classification of Non-Affine Non-Hecke Dynamical R-Matrices
• Zero modes of the SU(2)_k Wess-Zumino-Novikov-Witten model in Euler angles parametrization