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Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra
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Xiangqian Guo
,
Rencai Lu
Published/Copyright:
April 23, 2010
Abstract
This paper classifies irreducible Harish-Chandra modules over the loop-Virasoro algebra, which turn out to be highest weight modules, lowest weight modules and evaluation modules of the intermediate series (all wight spaces are 1-dimensional). As a by-product, we obtain a classification of irreducible Harish-Chandra modules over truncated Virasoro algebras. We also establish an irreducibility criterion for Verma modules over the loop Virasoro algebra and determine necessary and sufficient conditions for the simple quotient of a Verma module to be a Harish-Chandra module.
Received: 2009-08-02
Revised: 2009-12-01
Published Online: 2010-04-23
Published in Print: 2011-September
© de Gruyter 2011
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Articles in the same Issue
- Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field
- On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
- Wolff potentials and the 3-d wave operator
- Statistics for low-lying zeros of symmetric power L-functions in the level aspect
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- On the classification of fake lens spaces
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