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We derive a microscopic model describing the low-lying edge excitations inthe fractional quantum Hall liquid with $\nu=\frac{\nu^*} {\tilde\phi\nu^*+1}$.For $\nu^*>0$, it is found that the composite fermion model reduces to anSU$(\nu^*)$ Calogero-Sutherland model in a dimension reduction, whereas it isnot exact soluble for $\nu^*<0$. However, the ground states in both cases canbe found and the low-lying excitations can be shown the chiral Luttinger liquidbehaviors. On the other hand, we shows that the finite temperature behavior of$G-T$ curve will deviate from the prediction of the chiral Luttinger liquid. Wealso point out that the suppression of the `spin' degrees of freedom agreeswith very recent experiments by Chang et al. The two-boson model of Lee and Wenis described microscopically.Comment: 4 pages, Revtex, accepted for publication by PR

From composite fermions to the Calogero-Sutherland model: Edge of the fractional quantum Hall liquid and the dimension reduction