Quantum continuous $\mathfrak{gl}_{\infty}$: Tensor products of Fock modules and $\mathcal{W}_{n}$-characters

@article{Feigin2011QuantumC,
  title={Quantum continuous \$\mathfrak\{gl\}_\{\infty\}\$: Tensor products of Fock modules and \$\mathcal\{W\}_\{n\}\$-characters},
  author={B. Feigin and E. Feigin and M. Jimbo and T. Miwa and E. Mukhin},
  journal={Journal of Mathematics of Kyoto University},
  year={2011},
  volume={51},
  pages={365-392}
}
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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