New statistical properties of dark matter halos in Lagrangian space are presented. Tracing back the dark matter particles constituting bound halos resolved in a series of N-body simulations, we measure quantitatively the correlations of the proto-halos inertia tensors with the local tidal tensors and investigate how the correlation strength depends on the proto-halos sphericity, local density and filtering scale. It is shown that the majority of the proto-halos exhibit strong correlations between the two tensors provided that the tidal field is smoothed on the proto-halos mass scale. The correlation strength is found to increase as the proto-halos sphericity increases, as the proto-halos mass increases, and as the local density becomes close to the critical value, delta_{ec}. It is also found that those peculiar proto-halos which exhibit exceptionally weak correlations between the two tensors tend to acquire higher specific angular momentum in Eulerian space, which is consistent with the linear tidal torque theory. In the light of our results, it is intriguing to speculate a hypothesis that the low surface brightness galaxies observed at present epoch correspond to the peculiar proto-halos with extreme low-sphericity whose inertia tensors are weakly correlated with the local tidal tensors.
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