Composite-fermion description of rotating Bose gases at low angular momenta

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We study the composite fermion construction at and below the single vortex (L=N) state of weakly interacting rotating Bose gases, presenting a new method for handling the large number of derivatives typically occurring via the Slater determinant. Remarkably, the CF wave function at L=N becomes exact in the large N limit, even though this construction is not, a priori, expected to work in the low angular momentum regime. This implies an interesting mathematical identity which may be useful in other contexts.