Abstract : We construct a universal Vertex-IRF transformation between Vertex type universal solution and Face type universal solution of the quantum dynamical Yang-Baxter equation, in the finite dimensional and affine case. In the fundamental evaluation representation of Uq(A1(1)), this object is equal to standard Vertex-IRF transformation introduced by Baxter in his study of 8-vertex model. This universal Vertex-IRF transformation satisfies the Quantum Dynamical coBoundary equation. This solution has a simple Gauss decomposition which appears to be intimately related to the structure of quantum version of Whittaker vectors. We will present the consequences of our algebraic structures in the study of Whittaker Functions.