Some applications and constructions of intertwining operators in LCFT

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We discuss some applications of fusion rules and intertwining operators in the representation theory of cyclic orbifolds of the triplet vertex operator algebra.

• We prove that the classification of irreducible modules for the orbifold vertex algebra W(p)^{A_m} follows from a conjectural fusion rules formula for the singlet vertex algebra modules.
• In the p=2 case, we computed fusion rules for the irreducible singlet vertex algebra modules by using intertwining operators.
• This result implies the classification of irreducible modules for W(2)^{A_m}, conjectured previously in [4].