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

Abstract

In this paper, it is shown that the diagonal coset vertex operator algebra C(Lg(k+2,0),Lg(k,0)⊗Lg(2,0)) is rational and C2-cofinite in case g=so(2n), n≥3 and k is an admissible number for gˆ. It is also shown that the diagonal coset vertex operator algebra C(Lsl2(k+4,0),Lsl2(k,0)⊗Lsl2(4,0)) is rational and C2-cofinite in case k is an admissible number for sl2ˆ. Furthermore, irreducible modules of C(Lsl2(k+4,0),Lsl2(k,0)⊗Lsl2(4,0)) are classified in case k is a positive odd integer.