Categories of weight modules for unrolled restricted quantum groups at roots of unity

DOI10.4213/IM9234EarXiv1910.05922OpenAlexW4381306257MaRDI QIDQ6137455

Author name not available (Why is that?)

Publication date: 2 September 2023

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Abstract: Motivated by connections to the singlet vertex operator algebra in the

m a t h f r a k g = m a t h f r a k {s l}_{2}

case, we study the unrolled restricted quantum groups

o v e r l i n e U_{q}^{H} (m a t h f r a k g)

at arbitrary roots of unity with a focus on its category of weight modules. We show that the braid group action on the Drinfeld-Jimbo algebra

U_{q} (m a t h f r a k g)

naturally extends to the unrolled quantum groups and that the category of weight modules is a generically semi-simple ribbon category (previously known only for odd roots) with trivial M"{u}ger center. Projective covers of simple modules are shown to be self-dual, and some preliminary connections to the higher rank singlet vertex operator algebras are motivated.

Full work available at URL: https://arxiv.org/abs/1910.05922

zbMATH Keywords

quantum groups representation theory unrolled quantum groups

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups (quantized function algebras) and their representations (20G42)