q - Difference Intertwining Operators for Uq(sl(4)) and q - Conformal Invariant Equations

Consider a Lie group G,e.g., the Lorentz, Poincaré,conformal groups,and differential equations 1.1$$ \mathcal{I}\;f = j $$ which are G-invariant. These play a very important role in the description of physical symmetries - recall, e.g., the examples of Dirac, Maxwell equations, (for more examples cf., e.g., [1]). It is important to construct systematically such equations for the setting of quantum groups. Such equations there are expected as q-difference equations. The hope is that these equations will have less singular behaviour than the classical counterparts.