On dynamical adjoint functor

TL;DR

This paper establishes a formula connecting dynamical adjoint functors and twists over nonabelian bases, with applications to invariant star products on projective spaces.

Contribution

It provides an explicit relation between dynamical adjoint functors, dynamical twists, and invariant pairings on parabolic Verma modules, with concrete examples for $U(sl(n))$.

Findings

Derived an explicit formula linking dynamical adjoint functors and twists.

Constructed invariant star products on projective spaces for $U(sl(n))$ and $U_ abla(sl(n))$.

Demonstrated the application of the formula to specific algebraic structures.

Abstract

We give an explicit formula relating the dynamical adjoint functor and dynamical twist over nonalbelian base to the invariant pairing on parabolic Verma modules. As an illustration, we give explicit $U(sl(n))$- and $U_\hbar(sl(n))$-invariant star product on projective spaces.