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

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

2010-02-16

arxiv.org/abs/1002.3113v1

Mathematics

Quantum Algebra

24 pages

Scientific paper

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.

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