1996/11/20 by Falk Rohsiepe, Rohsiepe, Falk · 7 citations
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/9611160
36 pages, LaTeX2e
arxiv created 1996/11/20 · openalex publication_date 1996/11/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the necessity to include so-called logarithmic operators in conformal field theories (Gurarie, 1993) at values of the central charge belonging to the logarithmic series c1,p=1-6(p-1)2/p, reducible but indecomposable representations of the Virasoro algebra are investigated, where L0 possesses a nontrivial Jordan decomposition. After studying `Jordan lowest weight modules', where L0 acts as a Jordan block on the lowest weight space (we focus on the rank two case), we turn to the more general case of extensions of a lowest weight module by another one, where again L0 cannot be diagonalized. The moduli space of such `staggered' modules is determined. Using the structure of the moduli space, very restrictive conditions on submodules of `Jordan Verma modules' (the generalization of the usual Verma modules) are derived. Furthermore, for any given lowest weight of a Jordan Verma module its `maximal preserving submodule' (the maximal submodule, such that the quotient module still is a Jordan lowest weight module) is determined. Finally, the representations of the W-algebra W(2,33) at central charge c=-2 are investigated yielding a rational logarithmic model.