Bose condensates at high angular momenta

We exploit the analogy with the quantum Hall (QH) system to study weakly interacting bosons in a harmonic trap. For a $\ensuremath{\delta}$-function interaction potential the ``yrast'' states with $Lg~N(N\ensuremath{-}1)$ are degenerate, and we show how this can be understood in terms of Haldane exclusion statistics. We present spectra for four and eight particles obtained by numerical and algebraic methods, and demonstrate how a more general hard-core potential lifts the degeneracies on the yrast line. The exact wave functions for $N=4$ are compared with trial states constructed from composite fermions (CF), and the possibility of using CF states to study the low L region at high N is discussed.