Integrable hierarchy for homogeneous realization of the toroidal Lie algebra ${\mathcal{L}}_{r+1}^{\mathrm{tor}}({\mathfrak{sl}}_{\ell })$

Chao-Zhong Wu, Yi Yang

Starting from a fairly explicit homogeneous realization of the toroidal Lie algebra $\mathcal{L}^{\tor}_{r+1}(\fsl_\ell)$ via a lattice vertex algebra, we derive an integrable hier…