Quantum continuous $g{l}_{\infty }$: Tensor products of Fock modules and $W_n$ characters

Abstract

We construct a family of irreducible representations of the quantum continuous $g{l}_{\infty }$ whose characters coincide with the characters of representations in the minimal models of the $W_n$ algebras of $g{l}_n$ 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.

24 pages

References in corpus (2)

• A commutative algebra on degenerate CP^1 and Macdonald polynomials
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations

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