Frobenius reciprocity theorem and vertex operator algebras

Let $V$ be a vertex operator, $G$ a finite subgroup of $Aut(V)$ and $K$ a sub group of $G$, Set $H=\mathbb{C}[G]$ and $H’=\mathbb{C}[K]$, the group algebra of $G,K$ respectively. We define an induction functor from $VH$-modules category to $VH$-modules category, Frobenius reciprocity theorem are investigated. Using this induction functor, we give an explicit construction of admissible $VH$-modules from admissible $V$-modules. At last, we give a complete set of irreducible inequivalent admissible $VH$-modules.