In our project we plan to investigate several fundamental equations in Clifford analysis from a group theoretical point of view, studying the invariance of those equations (and thus also the solutions) under the action of (subgroups of) the orthogonal or unitary group (spin groups). This will lead to systems of PDEs with variable coefficients defined in lower dimensions, the standard example being the Vekua system in the plane. We also intend to study special solutions of these generalized Vekua systems giving rise to new types of Bessel functions, Hermite polynomials, Laguerre polynomials and other special functions.