Cosets of the $\mathcal{W}^k(\mathfrak{sl}_4, f_{\text{subreg}})$-algebra

@article{Creutzig2017CosetsOT,
  title={Cosets of the \$\mathcal\{W\}^k(\mathfrak\{sl\}\_4, f\_\{\text\{subreg\}\})\$-algebra},
  author={Thomas Creutzig and Andrew R. Linshaw},
  journal={arXiv: Representation Theory},
  year={2017}
}
Let $\mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}})$ be the universal $\mathcal{W}$-algebra associated to $\mathfrak{sl}_4$ with its subregular nilpotent element, and let $\mathcal {W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ be its simple quotient. There is a Heisenberg subalgebra $\mathcal{H}$, and we denote by $\mathcal{C}^k$ the coset $\text{Com}(\mathcal{H}, \mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}}))$, and by $\mathcal{C}_k$ its simple quotient. We show that for $k=-4+(m+4)/3… Expand
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