English

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 Lk(sl2)L_k(\mathfrak{sl}_2) at any non-integral admissible level kk. In particular, we show that the principal block of the category of weight modules over admissible Lk(sl2)L_k(\mathfrak{sl}_2) 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}
}