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

Abstract

We construct a family of irreducible representations of the quantum continuous ${\mathfrak{gl}}_{\infty }$ whose characters coincide with the characters of representations in the minimal models of the ${\mathcal{W}}_n$-algebras of ${\mathfrak{gl}}_n$ type. In particular, we obtain a simple combinatorial model for all representations of the ${\mathcal{W}}_n$-algebras appearing in the minimal models in terms of $n$ interrelating partitions.