| Summary: | Low-energy transport in quantum Hall states is carried through edge modes and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here, we show how the presence or breaking of symmetries of the edge Hamiltonian underlie transport properties, specifically dc conductance and noise. We demonstrate this through the analysis of hole-conjugate states of the quantum Hall effect, specifically the ν=2/3 case in a quantum point-contact geometry. We identify two symmetries, a continuous SU(3) symmetry and a discrete Z_{3} symmetry, whose presence or absence (different symmetry scenarios) dictate qualitatively different types of behavior of conductance and shot noise. While recent measurements are consistent with one of these symmetry scenarios, others can be realized in future experiments.
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