Boson and differential realizations of polynomial angular momentum algebra

The inhomogeneous multiboson and multivariable differential realizations of the polynomial angular momentum algebra of quadratic type, L-2, which may be seen as the nonlinear extension of an ordinary angular momentum algebra su(2) or its noncompact form su(1,1), are obtained from Fock representations of L-2, which are related to master representation of L-2 on the space of its universal enveloping algebra U(L-2) or to induced representations on their respective quotient spaces U(L-2)/I-i with different left ideals I-i. (C) 2001 American Institute of Physics.