Weight representations of affine Kac-Moody algebras and small quantum groups

Arakawa T, Creutzig T, Kawasetsu K (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Advances in Mathematics Elsevier

Book Volume: 477

Article Number: 110365

DOI: 10.1016/j.aim.2025.110365

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) at any non-integral admissible level k. In particular, we show that the principal block of the category of weight modules over admissible Lk(sl2) is equivalent to that of the corresponding (unrolled) small quantum group.

Authors with CRIS profile

Thomas Creutzig Lehrstuhl für Darstellungstheorie

Involved external institutions

Kumamoto University / 熊本大学 JP Japan (JP)

How to cite

APA:

Arakawa, T., Creutzig, T., & Kawasetsu, K. (2025). Weight representations of affine Kac-Moody algebras and small quantum groups. Advances in Mathematics, 477. https://doi.org/10.1016/j.aim.2025.110365

MLA:

Arakawa, Tomoyuki, Thomas Creutzig, and Kazuya Kawasetsu. "Weight representations of affine Kac-Moody algebras and small quantum groups." Advances in Mathematics 477 (2025).

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