Reduction of the Knizhnik-Zamolodchikov Equation - a Way of Producing Virasoro Algebra Singular Vectors

1992/07/10 by Alexander Ganchev, A. Ch. Ganchev, V. B. Petkova · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1016/0370-2693(92)91480-w

published as Phys.Lett. B293 (1992) 56-66 · 12 pages, plain TeX, SISSA-111/92/EP

arxiv created 1992/07/10 · openalex publication_date 1992/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the sl(2,C) KZ equation for (half-) integer isospins recovers, up to a gauge transformation, the matrix system for Virasoro algebra singular vectors of Bauer et al. In the case of Kac-Kazhdan spins the general (infinite matrix) KZ system is truncated due to the decoupling of the A^(1)₁ singular vectors. This suggests an algorithm converting Malikov-Feigin-Fuks singular vectors into Virasoro ones.

Citations

• Current algebra and Wess-Zumino model in two dimensions
• Infinite conformal symmetry in two-dimensional quantum field theory

Cited by

• Singular vectors and topological theories from Virasoro constraints via the Kontsevich-Miwa transform
• Analytic expressions for singular vectors of theN=2 superconformal algebra