This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost cyclostationary, and we give give some remarks concerning the historical development of the two nomenclatures. In this paper we survey the spectral theory of the covariance, the estimation of the Fourie...

We investigate classical spin systems in d≥1 dimensions whose transfer operator commutes with the action of a nonamenable unitary representation of a symmetry group, here SO(1, N); these systems may alternatively be interpreted as systems of interacting quantum mechanical particles moving on hyperbolic spaces. In sharp contrast to the analogous situation with a compact symmetry group the follow...

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group Bn for every n ≥ 2. If we view such an operator as a quantumcomputational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically...

We show that there is a homotopy cofiber sequence of spectra relating Carlsson’s deformation K-theory of a group G to its “deformation representation ring,” analogous to the Bott periodicity sequence relating connective K-theory to ordinary homology. We then apply this to study simultaneous similarity of unitary matrices. The algebraic K-theory of a category uses the machinery of infinite loop ...

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...

The irreducibility of a representation of a real Lie algebra may depend on whether the representation space is a real or complex Hilbert space. The unitary projective representations of the Poincare group on complex Hilbert spaces were studied by Wigner and many others. Although the Poincare group has a real Lie algebra, we do not know of any study of the orthogonal projective representations o...

We show that for a special class of geometric quantizations with “small” quantum errors, the classical correspondence gives rise to an asymptotic projective unitary representation group Hamiltonian diffeomorphisms. As application, we get obstruction actions finitely presented groups.

Using the holographic machinery built up in a previous work, we show that the hidden SL(2,R) symmetry of a scalar quantum field propagating in a Rindler spacetime admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra defined in the Fock representation. That representation has central charge c = 1. The Virasoro algebra of operators gets a manifest geometr...

Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P = L N be its Shilov boundary parabolic subgroup. This paper attaches an irreducible unitary representation of G to each of the (finitely many) L-orbits on n*. The Hilbert space of the representation consists of functions on the orbit which are square-integrable with respect to a certain L-equivariant...