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A variety of precise experiments have been carried out to establish the character of the superconducting state in Sr2RuO4. Many of these appear to imply contradictory conclusions concerning the symmetries of this state. Here, we propose that these results can be reconciled if we assume that there is a near-degeneracy between a d_{x^2-y^2} (B_{1g} in group theory nomenclature) and a g_{xy(x^2-y^2)} (A_{2g}) superconducting state. From a weak-coupling perspective, such an accidental degeneracy can occur at a point at which a balance between the on-site and nearest-neighbor repulsions triggers a d-wave to g-wave transition.

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