Hermitean oscillator-like realizations of classical algebras and superalgebras in Hilbert space with positive definite metric

The hermitean oscillator-like realizations of classical algebras in terms of bosonic and fermionic creation and annihilation operators are given. The hermitean realizations of classical superalgebras using boson-fermion oscillators are explicitly described. The assumption of positive definite metric in a Hilbert space of the oscillator states is exploited. Due to this fact, the realizations of superalgebras in the Hilbert space can be constructed only for: the real orthosymplectic superalgebra osp(N;2M;R); the unitary compact superalgebra su(N;M); the unitary noncompact one su(N;N;K;M); and the quaternionic unitary superalgebra uusub(α)(N;M;H). (author)