  Using high magnetic fields up to 60 T, we report magneto-transport and
photoluminescence (PL) studies of a two-dimensional electron gas (2DEG) in a
GaN/AlGaN heterojunction grown by molecular-beam epitaxy. Transport
measurements demonstrate that the quantum limit can be exceeded (Landau level
filling factor $\nu < 1$), and show evidence for the $\nu =2/3$ fractional
quantum Hall state. Simultaneous optical and transport measurements reveal
synchronous quantum oscillations of both the PL intensity and longitudinal
resistivity in the integer quantum Hall regime. PL spectra directly reveal the
dispersion of occupied Landau levels in the 2DEG and therefore the electron
mass. These results demonstrate the utility of high (pulsed) magnetic fields
for detailed measurements of quantum phenomena in high-density 2DEGs.
