Twisting Functors for Quantum Group Modules

TL;DR

This paper develops twisting functors for quantum group modules, establishing their properties and applications, including braid relations and impacts on Verma modules, over various algebraic settings.

Contribution

It provides a rigorous definition of twisting functors for quantum groups and proves they satisfy braid relations, extending their applicability.

Findings

Twisting functors are well-defined over $ ext{Q}(v)$ and $ ext{Z}[v,v^{-1}]$-algebras.

They satisfy braid relations, confirming their algebraic consistency.

Applications to Verma modules demonstrate their usefulness in representation theory.

Abstract

We construct twisting functors for quantum group modules. First over the field $\mathbb{Q}(v)$ but later over any $\mathbb{Z} [v,v^{-1}]$-algebra. The main results in this paper are a rigerous definition of these functors, a proof that they satisfy braid relations and applications to Verma modules.