1999/06/24 by Z. Bajnok, Zoltán Bajnok, Bajnok, Z. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9906185
22 pages, LaTeX, Extended version of the talk presented at CFT and Integrable models, Budapest, 1996
arxiv created 1999/06/24 · openalex publication_date 1999/06/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new approach to the study of the correlation functions of W-algebras. The conformal blocks (chiral correlation functions), for fixed arguments, are defined to be those linear functionals on the product of the highest weight (h.w.) representation spaces which satisfy the Ward identities. First we investigate the dimension of the chiral correlation functions in the case when there is no singular vector in any of the representations. Then we pass to the analysis of the completely degenerate representations. A special subspace of the h.w. representation spaces, introduced by Nahm, plays an important role in the considerations. The structure of these subspaces shows a deep connection with the quantum and classical Toda models and relates certain completely degenerate representations of the \wg algebra to representations of G. This is confirmed by an analysis for the Virasoro, \wa2 and \wbc2 algebra. We also relate our work to Nahms, Feigen-Fuchs' and Watts' results.