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- Title
Generalized Verma Modules over Lie Algebras of Weyl Type.
- Authors
Bin Xin; Yuezhu Wu
- Abstract
For a field 픽 of characteristic 0 and an additive subgroup Γ of 픽, there corresponds a Lie algebra $\widehat{{\cal W}}(\Gamma)$ of generalized Weyl type. Given a total order of Γ and a weight Λ, a generalized Verma $\widehat{{\cal W}}(\Gamma)$-module M(Λ, ≺) is defined. In this paper, the irreducibility of M(Λ, ≺) is completely determined. It is also proved that an irreducible highest weight module over the $\cal W$-infinity algebra ${\cal W}_{1+\infty}$ is quasifinite if and only if it is a proper quotient of a Verma module.
- Subjects
VERMA modules; MODULES (Algebra); WEYL groups; ALGEBRA; GROUP theory
- Publication
Algebra Colloquium, 2009, Vol 16, Issue 1, p131
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386709000157