Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras.

In this paper, under the assumption that the diagonal coset vertex operator algebra C (L g (k + l , 0) , L g (k , 0) ⊗ L g (l , 0)) is rational and C 2 -cofinite, the global dimension of C (L g (k + l , 0) , L g (k , 0) ⊗ L g (l , 0)) is obtained and the quantum dimensions of multiplicity spaces viewed as C (L g (k + l , 0) , L g (k , 0) ⊗ L g (l , 0)) -modules are also obtained. As an application, a method to classify irreducible modules of C (L g (k + l , 0) , L g (k , 0) ⊗ L g (l , 0)) is provided. As an example, we prove that the diagonal coset vertex operator algebra C (L E 8 (k + 2 , 0) , L E 8 (k , 0) ⊗ L E 8 (2 , 0)) is rational, C 2 -cofinite, and classify irreducible modules of C (L E 8 (k + 2 , 0) , L E 8 (k , 0) ⊗ L E 8 (2 , 0)) . [ABSTRACT FROM AUTHOR]