Hidden symmetry and correlated states of electrons and holes in quantum dots

We describe hidden symmetry and its application to the construction of exact correlated states of electrons and holes in quantum dots. The hidden symmetry is related to degenerate single particle energy shells and symmetric interactions. Both can be engineered in a quantum dot. We focus on hidden symmetry involving spin singlet pairing of electrons and spin singlet pairing of holes. Detailed calculations for a third shell are presented to illustrate the mechanism of pairing.