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Verma modules over generalized Virasoro algebras Vir[G]

✍ Scribed by Jun Hu; Xian-Dong Wang; Kai-Ming Zhao

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
116 KB
Volume
177
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let F be a ΓΏeld of characteristic 0, not necessarily algebraically closed, and G be an additive subgroup of F. For any total order on G which is compatible with the group addition, and for any Δ‹; h ∈ F, a Verma module M ( Δ‹; h) over the generalized Virasoro algebra Vir[G] is deΓΏned. In the present paper, the irreducibility of Verma modules M ( Δ‹; h) is completely determined.

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✍ Karen S. Brown πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 350 KB

Let g denote the Virasoro Lie algebra, h its Cartan subalgebra, and S(h) the symmetric algebra on h. In this paper we consider "thickened" Verma modules M(Ξ») which are (U (g), S(h))-bimodules satisfying M(Ξ») βŠ— S(h) C ∼ = M(Ξ») where M(Ξ») is the usual Verma module with highest weight Ξ» ∈ h \* . We det