The vertex algebra M(1)^+ and certain affine vertex algebras of level -1

Details The vertex algebra M(1)^+ and certain affine vertex algebras of level -1 The vertex algebra M(1)^+ and certain affine vertex algebras of level -1

2010-06-09

arxiv.org/abs/1006.1752v1

Mathematics

Quantum Algebra

20 pages

Scientific paper

We give a coset realization of the vertex operator algebra M(1)^+ with central charge \ell. We realize M(1)^+ as a commutant of certain affine vertex algebras of level -1 in the vertex algebra $L_{C_{\ell} ^{(1)}}(-\tfrac{1}{2}\Lambda_0) \otimes L_{C_{\ell} ^{(1)}}(-\tfrac{1}{2}\Lambda_0)$. We show that the simple vertex algebra L_{C_{\ell} ^{(1)}}(-\Lambda_0) can be (conformally) embedded into L_{A_{2 \ell -1} ^{(1)}} (-\Lambda_0) and find the corresponding decomposition. We also study certain coset subalgebras inside L_{C_{\ell} ^{(1)}}(-\Lambda_0).

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