Fraction representations and highest-weight-like representations of the Virasoro algebra
TLDR
In this paper, the necessary and sufficient conditions for fraction modules to be irreducible are determined, and the necessary conditions for two isomorphic fraction modules over centerless Virasoro algebra V to be isomorphic.About:
This article is published in Journal of Algebra.The article was published on 2013-08-01 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Verma module & Generalized Verma module.read more
Citations
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Simple Virasoro modules which are locally finite over a positive part
Volodymyr Mazorchuk,Kaiming Zhao +1 more
TL;DR: In this paper, a general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules is proposed, which enables us to classify all simple VMs that are locally finite over a positive part, using simple modules over a family of finite dimensional solvable Lie algebras.
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Irreducible Virasoro modules from irreducible Weyl modules
TL;DR: In this article, the authors used Block's results to classify irreducible modules over the differential operator algebra C [ t, t − 1, d d t ] and used the twisting technique to construct a class of modules A b over the Virasoro algebra for any b ∈ C.
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Wn+- and Wn-module structures on U(hn)
TL;DR: In this article, the authors classify the modules over W n + and W n n which are free U ( h n ) -modules of rank 1. And they show that the modules of W n+ are the W n -modules for some Λ n ∈ ( C ⁎ ) n and some a ∈ C.
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Simple Virasoro modules induced from codimension one subalgebras of the positive part
TL;DR: In this article, a new five-parameter family of simple modules over the Virasoro Lie algebra is constructed, which is based on the simple modules constructed in this paper.
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Tensor product weight modules over the Virasoro algebra
TL;DR: The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang as mentioned in this paper, who determined the necessary and sufficient conditions for these tensor products to be simple.
References
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Book
Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
Victor G. Kac,A. K. Raina +1 more
TL;DR: A collection of a series of lectures given by Prof. V Kac at the Tata Institute, India in Dec '85 and Jan '86 is presented in this article, where the authors focus on the idea of a highest weight representation, which goes through four different incarnations.
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Classification of Harish-Chandra modules over the Virasoro Lie algebra
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The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra
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Whittaker modules for the virasoro algebra
Matthew Ondrus,Emilie Wiesner +1 more
TL;DR: In this paper, the authors define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple WMs by central characters and composition series for general WMs.
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Representations of the Virasoro Algebra, I
TL;DR: In this paper, the structure of the tenser product of two isomorphic irreducible modules over the Virasoro algebra is studied case by case, and the subquotients of V + and V − are studied.
Related Papers (5)
Simple Virasoro modules which are locally finite over a positive part
Volodymyr Mazorchuk,Kaiming Zhao +1 more