Group projection method in statistical systems

We discuss an application of group theoretical methods to the formulation of the thermodynamics of systems constrained by the conservation laws described by a semi--simple compact Lie group. A general projection method that allows to construct a partition function for a given irreducible representation of the Lie group is outlined. Applications of the method in Lattice Gauge Theory (LGT) for non--zero baryon number and in the phenomenological description of particle production in ultrarelativistic heavy ion collisions are also indicated.