Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model

Abstract

The zero modes' Fock space for the extended chiral $su(2)$ WZNW model gives room to a realization of the Grothendieck fusion ring of representations of the restricted $U_{q}sl(2)$ quantum universal enveloping algebra (QUEA) at an even ($2h$-th) root of unity, and of its extension by the Lusztig operators. It is shown that expressing the Drinfeld images of canonical characters in terms of Chebyshev polynomials of the Casimir invariant $C$ allows a streamlined derivation of the characteristic equation of $C$ from the defining relations of the restricted QUEA. The properties of the fusion ring of the Lusztig's extension of the QUEA in the zero modes' Fock space are related to the braiding properties of correlation functions of primary fields of the extended $su(2{)}_{h-2}$ current algebra model.

36 pages, 1 figure; version 3 - improvements in Sec. 2 and 3: definitions of the double, as well as R- (and M-)matrix changed to fit the zero modes' ones

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Cited by in corpus (8)

• Factorizable ribbon quantum groups in logarithmic conformal field theories
• A note on the logarithmic (p,p') fusion
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality
• A differential U-module algebra for U=U_q sl(2) at an even root of unity
• Quantum su(n)_k monodromy matrices
• Quantum-sl(2) action on a divided-power quantum plane at even roots of unity
• Extended su(2)_k and restricted U_q sl(2)