Pathspace Decompositions for the Virasoro Algerba and Its Verma Modules
نویسنده
چکیده
Starting from a detailed analysis of the structure of pathspaces of the A-fusion graphs and the corresponding irreducible Virasoro algebra quotients V (c, h) for the (2, q odd) models, we introduce the notion of an admissible pathspace representation. The pathspaces PA over the A-Graphs are isomorphic to the pathspaces over Coxeter A-graphs that appear in FB models. We give explicit construction algorithms for admissible representations. From the finitedimensional results of these algorithms we derive a decomposition of V (c, h) into its positive and negative definite subspaces w.r.t. the Shapovalov form and the corresponding signature characters. Finally, we treat the Virasoro operation on the lattice induced by admissible representations adopting a particle point of view. We use this analysis to decompose the Virasoro algebra generators themselves. This decomposition also takes the nonunitarity of the (2, q) models into account. ∗ [email protected]
منابع مشابه
Verma modules over the generalized Heisenberg-Virasoro algebra
For any additive subgroup G of an arbitrary field F of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra L[G]. Given a total order of G compatible with its group structure, and any h, hI , c, cI , cLI ∈ F, a Verma module M̃(h, hI , c, cI , cLI) over L[G] is defined. In the this note, the irreducibility of Verma modules M̃(h, hI , c, cI , cLI) is completely determined.
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