  To discuss a possibility that the superconductivities in Na_xCoO_2yH_2O are
induced by the electron correlation, we investigate the possible pairing
symmetry based on the single-band Hubbard model whose dispersion of the bare
energy band is obtained by using FLAPW-LDA band structure calculation of
Na_xCoO_2yH_2O. The superconducting transition temperature is estimated by
solving the Eliashberg equation. In this equation, both normal and anomalous
self-energies are calculated up to the third-order terms with respect to the
Coulomb repulsion. In the case of spin-singlet pairing, the candidate of
pairing symmetry (the maximum eigen value \lambda_max^SS of Eliashberg's
equation) belongs to d-wave(E_2 representation of D_6 group). In the case of
spin-triplet pairing, the candidate of pairing symmetry (the maximum eigen
value \lambda_max^ST of Eliashberg's equation) belongs to
f_{y(y^{2}-3x^{2})}-wave (B_1 representation of D_6 group). It is found that
\lambda_max^SS\simeq\lambda_max^ST and the transition temperatures of
unconventional pairing state are estimated to be low compared with observed
temperature within our simple model.
