Current algebras and categorified quantum groups

@article{Beliakova2017CurrentAA,
  title={Current algebras and categorified quantum groups},
  author={A. Beliakova and K. Habiro and Aaron D. Lauda and B. Webster},
  journal={J. Lond. Math. Soc.},
  year={2017},
  volume={95},
  pages={248-276}
}
We identify the trace, or 0th Hochschild homology, of type ADE categorified quantum groups with the corresponding current algebra of the same type. To prove this, we show that 2-representations defined using categories of modules over cyclotomic (or deformed cyclotomic) quotients of KLR-algebras correspond to local (or global) Weyl modules. We also investigate the implications for centers of categories in 2-representations of categorified quantum groups. 
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