Counting minimal form factors of the restricted sine-Gordon model

2003/03/26 by M. Jimbo, Jimbo, M., T. Miwa +4 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.math-ph/0303059

58 pages, final version, Proposition 2.8 modified

openalex publication_date 2003/03/26 · arxiv created 2004/01/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of polynomials which enter the integral representation for form factors. This space may be viewed as a q-analog of the space of conformal coinvariants associated with U_q(sl₂^) with q=√(-1). We prove that its character is given by the restricted Kostka polynomial multiplied by a simple factor. As a result, we obtain a formula for the truncated character of the total space of local fields in terms of the Virasoro characters.

Citations

• On solutions of the KZ and qKZ equations at level zero
• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• A functional model for the tensor product of level 1 highest and level -1 lowest modules for the quantum affine algebra U_q(sl₂^)
• Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center

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