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We investigate the relation between broken time-reversal symmetry andlocalization of the electronic states, in the explicitly tractable case of theLandau model. We first review, for the reader's convenience, the symmetries ofthe Landau Hamiltonian and the relation of the latter with the Segal-Bargmannrepresentation of Quantum Mechanics. We then study the localization propertiesof the Landau eigenstates by applying an abstract version of the Balian-LowTheorem to the operators corresponding to the coordinates of the centre of thecyclotron orbit in the classical theory. Our proof of the Balian-Low Theorem,although based on Battle's main argument, has the advantage of beingrepresentation-independent.

Symmetry and localization for magnetic Schroedinger operators: Landau levels, Gabor frames and all that