Classification of Harish-Chandra Modules over the Higher Rank Virasoro Algebras

By Yu-cai Su. 2003

82 citations recorded by the source corpus.

We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is either a module of the intermediate series, or a finitely-dense module. As an application, it is also proved that an indecomposable weight module with finite weight multiplicities over a generalized Witt algebra is either a uniformly bounded module (i.e., a module with weight multiplicities uniformly bounded) with all nonzero weights having the same multiplicity, or a finitely-dense module, as long as the generalized Witt algebra satisfies one minor condition.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ec692007008b58e309ba66a8a6bc41cd2d9d3d56

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In Algebra and Number Theory

1. Shoulan Gao
2. Yu-cai Su
3. Kaiming Zhao
4. R. Lu

In Geometry and Topology

1. Shoulan Gao
2. Linsheng Zhu
3. Dong Liu
4. Yu-cai Su
5. Kaiming Zhao
6. R. Lu

In Statistical and Nonlinear Physics

1. Shoulan Gao
2. Linsheng Zhu
3. Dong Liu
4. Yu-cai Su

Citations in the corpus

• Quasifinite representations of a Lie algebra of Block type (2004, methodology): “[16]).”
• Classification of irreducible weight modules over W-algebra W(2,2) (2008, background): “Key Words: The the W -algebra W (2, 2), weight modules, support Mathematics Subject Classification (2000): 17B56; 17B68.”