Rationality and C2-cofiniteness of certain diagonal coset vertex operator algebras.

In this paper, it is shown that the diagonal coset vertex operator algebra C (L g (k + 2 , 0) , L g (k , 0) ⊗ L g (2 , 0)) is rational and C 2 -cofinite in case g = s o (2 n) , n ≥ 3 and k is an admissible number for g ˆ. It is also shown that the diagonal coset vertex operator algebra C (L s l 2 (k + 4 , 0) , L s l 2 (k , 0) ⊗ L s l 2 (4 , 0)) is rational and C 2 -cofinite in case k is an admissible number for s l 2 ˆ. Furthermore, irreducible modules of C (L s l 2 (k + 4 , 0) , L s l 2 (k , 0) ⊗ L s l 2 (4 , 0)) are classified in case k is a positive odd integer. [ABSTRACT FROM AUTHOR]