2007/10/31 by P. Furlan, Ludmil Hadjiivanov, L. Hadjiivanov +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1007/s11005-007-0209-4
published as Lett.Math.Phys.82:117-151,2007 · 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
openalex publication_date 2007/12/01 · arxiv created 2008/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Uq 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.