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2001•Communications in AlgebraRequires access

REPRESENTATIONS OF THE VERTEX ALGEBRA W 1+∞ WITH A NEGATIVE INTEGER CENTRAL CHARGE

Dražen Adamović

Open publisher page 16 citations

Abstract

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 central charge c = −N. We show that W 1+∞,−N is a subalgebra of the Heisenberg vertex algebra M(1) with 2N generators, and construct 2N-dimensional family of irreducible W 1+∞,−N -modules. Considering these modules as -modules, we identify the corresponding highest weights.

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What this paper is about

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 central charge c = −N. We show that W 1+∞,−N is a subalgebra of the Heisenberg vertex algebra M(1) with 2N generators, and construct 2N-dimensional family of irreducible W 1+∞,−N -modules. Considering these modules as -modules, we identify the corresponding highest weights.

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Available abstract

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 central charge c = −N. We show that W 1+∞,−N is a subalgebra of the Heisenberg vertex algebra M(1) with 2N generators, and construct 2N-dimensional family of irreducible W 1+∞,−N -modules. Considering these modules as -modules, we identify the corresponding highest weights.

Key concepts: Mathematics, Vertex operator algebra, Subalgebra, Vertex (graph theory), Central charge, Integer (computer science), Extension (predicate logic), Lie algebra

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