Current algebras and categorified quantum groups

Wednesday, 3 December, 2014

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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.


Anna Beliakova
Kazuo Habiro
Aaron D. Lauda
Ben Webster