More on super-replication formulae

We extend Norton–Borcherds–Koikeʹs replication formulae to super-replicable ones by working with the congruence groups Γ1(N) and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite-dimensional Lie superalgebras whose denominator identities coincide with the above product identities. Therefore it could be one way to find a connection between modular functions and infinite-dimensional Lie algebras.