The Vertex Algebra $M(1{)}^{+}$ and Certain Affine Vertex Algebras of Level -1

Abstract

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 $L_{C_{\ell }^{(1)}}(-\frac{1}{2}{\Lambda }_0)\otimes L_{C_{\ell }^{(1)}}(-\frac{1}{2}{\Lambda }_0)$. 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 $L_{C_{\ell }^{(1)}}(-{\Lambda }_0)$.

References in corpus (5)

• Vertex Algebras and Algebraic Curves
• Annihilating fields of standard modules of sl(2,C)~ and combinatorial identities
• The N=1 triplet vertex operator superalgebras
• Some Rational Vertex Algebras
• Representations of certain non-rational vertex operator algebras of affine type

Cited by in corpus (2)

• Cosets of affine vertex algebras inside larger structures
• Kostant's pair of Lie type and conformal embeddings