Current algebras and categorified quantum groups

Wednesday, 3 December, 2014

Published in: 

arXiv:1412.1417

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.

Author(s): 

Anna Beliakova
Kazuo Habiro
Aaron D. Lauda
Ben Webster