Twisting Functors for Quantum Group Modules

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.

39 pages