We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of real irreducible representations of unitary symmetries in the Nambu space. ...

ECENTLY, Gell-Mann' and Ne'eman have independently proposed a scheme, called the eightfold way, in which the eight baryons (ftT, A., Z, and ) are assumed to form a supermultiplet, degenerate in the limit of a certain symmetry, and split into the familiar isotopic multiplets by a dynamical interaction. The symmetry is called unitary symmetry and the relevant group is the group of unitary unimodu...

For each integer n ≥ 2, we demonstrate that a 2n-dimensional generalized MICZ-Kepler problem has an g Spin(2, 2n+1) dynamical symmetry which extends the manifest Spin(2n) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight g Spin(2, 2n+1)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest ...