INHOMOGENEOUS BOSON REALIZATION OF INDECOMPOSABLE REPRESENTATIONS OF LIE-ALGEBRAS

By making use of the differential realization of Lie algebras in the space of inhomogeneous polynomials of a certain number of variables, the corresponding inhomogeneous boson realization of Lie algebras is given. A new kind of indecomposable representations of Lie algebras are studied on the universal enveloping algebra of Heisenberg-Weyl algebra, its subspaces and its quotient spaces. The finite-dimensional representations are naturally obtained on the subspaces of Fock space. As an example, the indecomposable and irreducible representations of the Lie algebra su(2) are discussed in detail. © 1990 American Institute of Physics.