Quantum Groups for Restricted SOS Models

TL;DR

This paper introduces restricted dynamical quantum groups and explores their representation categories, which are monoidal and relate to $ ext{pi}$-graded vector spaces, advancing the mathematical framework of quantum groups.

Contribution

It defines restricted dynamical quantum groups via their representation categories, linking them to $ ext{pi}$-graded vector spaces, a novel conceptual development.

Findings

Established the structure of restricted dynamical quantum groups.

Connected their representation categories to $ ext{pi}$-graded vector spaces.

Provided a new framework for studying quantum groups.

Abstract

We introduce the notion of restricted dynamical quantum groups through their category of representations, which are monoidal categories with a forgetful functor to the category of $\pi$-graded vector spaces for a groupoid $\pi$.