We derive exact analytical results for the wave functions and energies of
harmonically trapped two-component Bose-Einstein condensates with weakly
repulsive interactions under rotation. The isospin symmetric wave functions are
universal and do not depend on the matrix elements of the two-body interaction.
The comparison with the results from numerical diagonalization shows that the
ground state and low-lying excitations consists of condensates of p-wave pairs
for repulsive contact interactions, Coulomb interactions, and the repulsive
interactions between aligned dipoles.Comment: 4 pages, 1 figure; revised version explains exact solutions in terms
of isospin symmetry and Hund's rul
