Chiral Symmetry in algebraic and analytic approaches

We compare among themselves two different methods for the derivation of results following from the requirement of polynomial boundedness of tree-level chiral amplitudes. It is shown that the results of the algebraic approach are valid also in the framework of the analytical one. This means that the system of Sum Rules and Bootstrap equations previously obtained with the help of the latter approach can be analyzed in terms of reducible representations of the unbroken Chiral group with the known structure of the mass matrix.