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We present a detailed theory of transport through line junctions formed bycounterpropagating single-branch fractional-quantum-Hall edge channels havingdifferent filling factors. Intriguing transport properties are exhibited whenstrong Coulomb interactions between electrons from the two edges are present.Such strongly correlated line junctions can be classified according to thevalue of an effective line-junction filling factor n that is the inverse of aneven integer. Interactions turn out to affect transport most importantly forn=1/2 and n=1/4. A particularly interesting case is n=1/4 corresponding to,e.g., a junction of edge channels having filling factor 1 and 1/5,respectively. We predict its differential tunneling conductance to oscillate asa function of voltage. This behavior directly reflects the existence of novelMajorana-fermion quasiparticle excitations in this type of line junction.Experimental accessibility of such systems in current cleaved-edge overgrownsamples enables direct testing of our theoretical predictions.Comment: 2 figures, 10 pages, RevTex4, v2: added second figure for clarit

Conductance oscillations in strongly correlated fractional quantum Hall line junctions