  The main problem in the Hamiltonian formulation of Lattice Gauge Theories is
the determination of an appropriate basis avoiding the over-completeness
arising from Mandelstam relations. We short-cut this problem using Harmonic
analysis on Lie-Groups and intertwining operators formalism to explicitly
construct a basis of the Hilbert space. Our analysis is based only on
properties of the tensor category of Lie-Group representations. The Hamiltonian
of such theories is calculated yielding a sparse matrix whose spectrum and
eigenstates could be exactly derived as functions of the coupling $g^2$
