Classification of irreducible weight modules over higher rank Virasoro algebras

Details Classification of irreducible weight modules over higher rank Virasoro algebras Classification of irreducible weight modules over higher rank Virasoro algebras

2003-08-14

arxiv.org/abs/math/0308133v3

Advances in Math., Vol.201(2), 630-656(2006)

Mathematics

Representation Theory

24 pages

Scientific paper

Let $G$ be a rank $n$ additive subgroup of $\bC$ and $\Vir[G]$ the corresponding Virasoro algebra of rank $n$. In the present paper, irreducible weight modules with finite dimensional weight spaces over $\Vir[G]$ are completely determined. There are two different classes of them. One class consists of simple modules of intermediate series whose weight spaces are all 1-dimensional. The other is constructed by using intermediate series modules over a Virasoro subalgebra of rank $n-1$. The classification of such modules over the classical Virasoro algebra was obtained by O. Mathieu in 1992 using a completely different approach.

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