We construct fermionic-bosonic representations for a class of generalized B(m, n), C(n), D(m, n)-graded Lie superalgebras coordinatized by quantum tori with nontrivial central extensions.
We construct a class of modules for the twisted multi-loop algebra of type A1 × A1 by applying Wakimoto free bosonic realization. We also discuss the structures and the irreducibility of the Fock space.