Boson representations of symplectic algebras

A reduction of the boson representation of the algebra of the noncompact groupSp(4k, R), k>0, to its subgroupSU(k) is realized. The reduction scheme has two main branches: one through the totally symmetric unitary representations of the maximal compact subalgebra u(2k); the other through the ladder representations of the noncompact subalgebrau(k, k). Both reductions are accomplished by means of the same set of Hermitian operators, but taken in different order. The case ofk=3, for the groupSp(12,R), used in the interacting vector boson model, is discussed in more detail.