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We analyze the effect that the Coulomb interaction has on the edgeexcitations of an electron gas confined in a bar of thickness $W$, and inpresence of a magnetic field corresponding to filling factor 1 Quantum Halleffect. We find that the long-range interaction between the edges leads thesystem to a ground state with a quasi-long range order, similar to a ChargeDensity Wave. The spectral density of states vanishes at zero frequency, andincreases with frequency faster than any power law, being the conductance of ainfinite long system zero.Comment: 10 pages, latex, 3 figures available by FAX upon request from  brey@marlene.fmc.uam.e

Charge Density Wave Behavior in the Integer Quantum Hall Effect Edge States