How to regularize singular vectors and kill the dynamical Weyl group
  We study the meromorphic family of intertwining operators between Verma modules and their products with finite-dimensional ones. A regularizing operator, acting in a finite dimensional module U, makes this family holomorphic, and conjugates the dynamical Weyl group operators to constant operators. We prove uniqueness property for regularizing operators, and construct them explicitly for the Lie algebra sl_3. 
K. Styrkas, V. Tarasov, A. Varchenko