• Corpus ID: 16393400

# W_1+∞ and W(gl_N) with central charge N

@inproceedings{Frenkel1994W\_1AW,
title={W\_1+∞ and W(gl\_N) with central charge N},
author={Edward Vladimir Frenkel and Victor G. Kac and Andrey Radul and W. Wang},
year={1994}
}
• Published 20 May 1994
• Mathematics
The Lie algebra D̂, which is the unique non-trivial central extension of the Lie algebra D of differential operators on the circle [KP1], has appeared recently in various models of two-dimensional quantum field theory and integrable systems, cf., e.g., [BK, FKN, PRS, IKS, CTZ, ASvM]. A systematic study of representation theory of the Lie algebra D̂, which is often referred to as W1+∞ algebra, was initiated in [KR]. In that paper irreducible quasi-finite highest weight representations of D̂ were…
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• 1996
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Q A ] 7 N ov 2 00 4 Representations of Centrally-Extended Lie Algebras over Differential Operators and Vertex Algebras 1
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of
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We show that there are exactly two anti-involutions σ± of the algebra of differential operators on the circle that are a multiple of p(t∂t) preserving the principal gradation (p∈C[x] non-constant).
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Let D be the Lie algebra of regular differential operators on , and be the central extension of D. Let W 1+∞,minus;N be the vertex algebra associated to the irreducible vacuum -module with the

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