Current algebras and categorified quantum groups
Quantum Algebra
2023-01-25 v3 Representation Theory
Abstract
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.
Cite
@article{arxiv.1412.1417,
title = {Current algebras and categorified quantum groups},
author = {Anna Beliakova and Kazuo Habiro and Aaron D. Lauda and Ben Webster},
journal= {arXiv preprint arXiv:1412.1417},
year = {2023}
}
Comments
28 pages, with tikz and xypic diagrams. v2: changed discussion of cyclicity to include all simply-laced Kac-Moody algebras. v3: revised final version. edited from journal version to fix some when ADE hypothesis is needed