Exact eigenstates for repulsive bosons in two dimensions

We consider a model of N two-dimensional bosons in a harmonic potential with weak repulsive delta -function interactions. We show analytically that, for angular momentum L less than or equal toN, the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates with energy N(N-L/2-1). Extensive numerical analysis confirms that these are actually the ground states, but we are currently unable to prove this analytically. The special case L=N can be thought of as the generalization of the usual superfluid one-vortex state to Bose-Einstein condensates in a trap.