Classification of simple weight Virasoro modules with a finite-dimensional weight space

Mazorchuk, Volodymyr; Zhao, Kaiming

doi:10.1016/j.jalgebra.2006.05.007

Cited by 53 publications

(46 citation statements)

References 6 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are two classical families of simple V-modules: highest weight modules (completely described in [FF]) and the so-called intermediate series modules. In [Mt] it is shown that these two families exhaust all simple weight Harish-Chandra modules, that is weight modules with finite dimensional weight spaces with respect to the Cartan subalgebra spanned by l 0 and c. In [MZ1] it is even shown that the above modules exhaust all simple weight modules admitting a nonzero finite dimensional weight space. Various other families of simple V-modules were studied in [Zh,OW1,LGZ,FJK,Ya,GLZ,OW2].…”

Section: Introduction and Formulation Of The Resultsmentioning

confidence: 99%

Simple Virasoro modules which are locally finite over a positive part

Mazorchuk

Zhao

2013

Sel. Math. New Ser.

Self Cite

117

View full text Add to dashboard Cite

Abstract. We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This reduces the problem of classification of simple Virasoro modules which are locally finite over a positive part to classification of simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras all simple modules are classified by R. Block and we extend this classification to the next member of the family. As a result we recover many known but also construct a lot of new simple Virasoro modules. We also propose a revision of the setup for study of Whittaker modules.

show abstract

Section: Introduction and Formulation Of The Resultsmentioning

confidence: 99%

Simple Virasoro modules which are locally finite over a positive part

Mazorchuk

Zhao

2013

Sel. Math. New Ser.

Self Cite

117

View full text Add to dashboard Cite

show abstract

“…Since some weight spaces of W (N 0 ) are infinite-dimensional, from [MZ1] we know that any nonzero weight spaces are infinite-dimensional. Thus (b) follows.…”

Section: Also This Map Induces An Isomorphismmentioning

confidence: 99%

Tensor product weight modules over the Virasoro algebra

Chen¹,

Guo

Zhao³

2013

Journal of the London Mathematical Society

Self Cite

View full text Add to dashboard Cite

Abstract. The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang [Z] in 1997. Since then the irreducibility problem for the tensor products has been open. In this paper, we determine the necessary and sufficient conditions for these tensor products to be simple. From non-simple tensor products, we can get other interesting simple Virasoro modules. We also obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modules and intermediate series modules are isomorphic respectively. Our method is to develop a "shifting technique" and to widely use Feigin-Fuchs' Theorem on singular vectors of Verma modules over the Virasoro algebra.

show abstract

“…Classical classes of simple weight V-modules are simple highest weight modules, see [FF], and intermediate series modules. Put together, these two classes exhaust all simple weight V-modules with finite dimensional weight spaces, see [Mt], and even those containing a finite dimensional weight space, see [MZ1]. We also refer the reader to the recent monograph [IK] for a detailed survey of the classical part of the representation theory of V. There are a number of other examples of simple V-modules constructed in [Zh,OW,GWZ,LGZ,MZ2] using various tricks.…”

Section: Introduction and Description Of The Resultsmentioning

confidence: 99%