Transformation Groups

, Volume 17, Issue 2, pp 547–570 | Cite as

Classification of irreducible quasifinite modules over map Virasoro algebras

  • Alistair SavageEmail author


We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir ⊗ A, where Vir is the Virasoro algebra and A is a finitely generated commutative associative unital algebra over the complex numbers. It is shown that all such modules are tensor products of generalized evaluation modules. We also give an explicit sufficient condition for a Verma module of Vir ⊗ A to be reducible. In the case that A is an infinite-dimensional integral domain, this condition is also necessary.


Weight Space Weight Module Verma Module High Weight Vector High Weight Module 
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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OttawaOttawaCanada

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