Basis of irreducible representations of orthogonal groups

A method for constructing a basis of irreducible representations of unitary groupsU_n is generalized to orthogonal groupsO_n. The corresponding algorithm is given for the chain for groupsU_n O_n and also for the chain which is of great relevance in physics.The constructed basis is used for the calculation of the fractional six-particle parentage coefficients for separation of one-, two- and three-particle wave functions. All possible states with excitation quantaN2 are taken into account. The present results, together with previous work, are used for the investigation of the six-quark system, in particular for calculating theD-state probability in the ground state of this system.