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The spectrum and degeneracies of the Dirac operator are analysed on compactcoset spaces when there is a non-zero homogeneous background gauge field whichis compatible with the symmetries of the space, in particular when the gaugefield is derived from the spin-connection. It is shown how the degeneracy ofthe lowest Landau level in the recently proposed higher dimensional quantumHall effect is related to the Atiyah-Singer index theorem for the Diracoperator on a compact coset space.Comment: 25 pages, typeset in LaTeX, uses youngtab.st

The spectrum of the Dirac operator on coset spaces with homogeneous gauge fields