Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

Details Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

2006-07-25

arxiv.org/abs/math/0607614v2

Mathematics

Representation Theory

14 pages

Scientific paper

Let $G$ be an arbitrary additive subgroup of $C$ and $Vir[G]$ the corresponding generalized Virasoro algebra. In the present paper, irreducible weight modules with finite dimensional weight spaces over $Vir[G]$ are completely determined. The classification strongly depends on the index group $G$. If $G$ does not have a direct summand $Z$, then such irreducible modules over $Vir[G]$ are only modules of intermediate series whose weight spaces are all 1-dimensional. Otherwise, there is one more class of modules which are constructed by using intermediate series modules over a generalized Virasoro subalgebra $Vir[G_0]$ of $Vir[G]$ for a direct summand $G_0$ of $G$ with corank 1.

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