ON COMBINATORIAL STRUCTURE OF STATE VECTORS IN U(N) .2. GENERALIZATION OF HYPERGEOMETRIC FUNCTIONS ON U (N) STATES

The derivation of the explicit algebraic expressions of the SU(n) state vectors in the boson-operator realization is shown to lead to a generalization of hypergeometric functions. The SU(3) state vectors are rederived by the combinatorial method - propounded in Paper I [J. Math. Phys. 10, 221 (1969)] of this series of papers - and are shown to be represented by a hypergeometric distribution function and an associated generalization of the Young tableaux calculus. The SU(4) state vectors are also derived to demonstrate the main features of the general U(n) state vectors. The SU(4) state vectors are expressed in terms of the constituents of Radon transforms.