Quantum continuous gl∞: Tensor products of Fock modules and Wn-characters

We construct a family of irreducible representations of the quantum continuous gl(infinity) whose characters coincide with the characters of representations in the minimal models of the W-n-algebras of gl(n) type. In particular, we obtain a simple combinatorial model for all representations of the W-n-algebras appearing in the minimal models in terms of n interrelating partitions.