Rank one polynomial modules over the quantum group of type A₁

Abstract

In this article, we classify all rank one polynomial modules over the quantum groups $U_q(\mathfrak{s}{\mathfrak{l}}_2)$ and ${\mathcal{U}}_q(\mathfrak{s}{\mathfrak{l}}_2)$ for generic q. We also provide the equivalent conditions for the simplicity of these modules.

Keywords:

• Polynomial module
• quantum group
• simple module

2020 Mathematics Subject Classification:

• 17B37