Representations of Vertex Operator Algebras $V_{L_2}^{S_4}$ and   $V_{L_2}^{A_5}$
  $C_2$ cofiniteness and rationality of $V_{L_2}^{S_4}$ are obtained, and irreducible $V_{L_2}^{S_4}$-modules are classified. With the assumption of rationality and $C_2$ cofiniteness, irreducible $V_{L_2}^{A_5}$-modules are determined. Also, quantum dimensions of these irreducible modules are calculated. 
Li Wu and Liuyi Zhang
math-ph math.MP math.QA