Irreducible *-representations of Lie superalgebras B(0,n) with finite-degenerated vacuum

The problem of obtaining irreducible * - representations π of Lie subalgebras B(O, n), n = 1, 2, starting with a recently constructed family of linear representations in terms of differential operators on the space Fsub(N)sup((n)) of Csup(N)-valued Csup(infinity)-functions is studied. Equivalent formulation via creation-annihilation operators of a para-Bose systems with n degrees of freedom is used. The domain D of any π is shown to be a subset of Fsub(N)sup((n)) containing a non-zero vacuum subspace. Necessary conditions are obtained and it is shown that each representation has a cyclic vector that is fully specified by real ν >= 0 and highest weight of sl(n, C). A basis in the domain D is constructed. It contains common eigen-vectors of particle-number operators corresponding to individual degrees of freedom of the para-Bose system under consideration