We preform a multi-orbital analysis on the novel superconductivity in NaxCoO2·yH2O. We construct a three-orbital model which reproduces the band structure expected from the LDA calculation. The effective interaction leading to the pairing is estimated by means of the perturbation theory. It is shown that the spin triplet superconductivity is stabilized in the wide parameter region. This is basically owing to the ferromagnetic character of spin fluctuation. The p-wave and f-wave superconductivity are nearly degenerate. The former is realized when the Hund's rule coupling is large, and vice versa. In a small part of the parameter space, the d-wave superconductivity is also stabilized. We point out that the orbital degeneracy plays an essential role for these results. In particular, the momentum dependence of wave function of quasi-particles is quite important. The nearly degeneracy of p-wave and f-wave superconductivity is explained by analysing the microscopic character of each Fermi surface. We discuss the validity of some reduced models. While the single-orbital Hubbard model reproducing the Fermi surface is qualitatively inappropriate, we find an effective two-orbital model appropriate for studying the superconductivity. We investigate the vertex corrections higher than the third order on the basis of the two-orbital model. It is shown that the vertex correction induces the screening effect but does not affect qualitative results.
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