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With the use of microscopic approaches, i.e., the algebraic version of the resonating group method employing the hyperspherical harmonic oscillator basis functions, the general properties of weakly bound light nuclei with the lowest three-body decay threshold are studied. As a way of truncating the basis space, the minimal approximation based on the Pauli-allowed harmonic oscillator basis states is proposed. For the case of the ^6He nucleus, the basis states are constructed, and the wave function of the ground state as well as the scattering S-matrix for the continuum spectrum is found. Although the exchange mixture parameter of the Minnesota potential is chosen rather large to fit the experimental ground state energy, all basic features of the system are well reproduced. The resonance behavior of the latter indicates that a 0^+ resonance state exists at 〜8 MeV over the threshold.Calculations of the probability of the monopole transition from the ground state to the continuum states confirm this result.