Quantum continuous $gl_\infty$: Tensor products of Fock modules and $W_n$ characters

TL;DR

This paper constructs irreducible representations of quantum continuous $gl_ $ that match the characters of minimal model representations of $W_n$ algebras, providing a combinatorial model via interrelating partitions.

Contribution

It introduces a new family of irreducible representations of quantum continuous $gl_ $ with characters matching $W_n$ minimal models, and offers a combinatorial description.

Findings

Characters coincide with $W_n$ minimal model characters

Provides a combinatorial model using interrelating partitions

Constructs explicit irreducible representations

Abstract

We construct a family of irreducible representations of the quantum continuous $gl_\infty$ 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.