Abstract
We show that possible forms for the density matrices of states of a two-dimensional electron gas (2D EG) are profoundly limited when the electrons are constrained to lie in the lowest Landau level. In particular for any number of particles the matrices may be expressed in terms of their diagonal elements in a position representation. The simplification which is known to occur for Hartree-Fock calculations in a single Landau level of the 2D EG is a specific consequence of this general property.
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