Weight representations of affine Kac-Moody algebras and small quantum groups
Representation Theory
2023-11-20 v1 Mathematical Physics
math.MP
Quantum Algebra
Abstract
We study the weight modules over affine Kac-Moody algebras from the view point of vertex algebras, and determine the abelian category of weight modules for the simple affine vertex algebra at any non-integral admissible level . In particular, we show that the principal block of the category of weight modules over admissible is equivalent to that of the corresponding (unrolled) small quantum group.
Keywords
Cite
@article{arxiv.2311.10233,
title = {Weight representations of affine Kac-Moody algebras and small quantum groups},
author = {Tomoyuki Arakawa and Thomas Creutzig and Kazuya Kawasetsu},
journal= {arXiv preprint arXiv:2311.10233},
year = {2023}
}