Founding harmonic analysis on classical simple complex groups, I.M. Gelfand and M.A. Naimark in their classical book [GN] posed three basic questions: unitary duals, characters of irreducible unitary representations and Plancherel measures. In the case of reductive p-adic groups, the only series of reductive groups where unitary duals are known are general linear groups. In this paper we reduce...

In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to...

For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of analytic vectors the same construction is possible and leads to a real analytic moment mapping.

Let φ be an isometric automorphism of the non-commutative disc algebra An for n ≥ 2. We show that every contractive covariant representation of (An, φ) dilates to a unitary covariant representation of (On, φ). Hence the C*-envelope of the semicrossed product An ×φ Z is On ×φ Z.

This study examines the effects on the stock market unitary risk premium and volatility associated with the listing of stock and stock index derivatives in Switzerland. Based on a univariate GARCH (1,1) specification of the stock index variance and a time-varying unitary risk premium representation, we can reject the hypothesis that stock and stock index derivatives listings do not affect the t...

Wightman functions for interacting quantum fields on curved space times are calculated via the perturbation theory of the Yang-Feldman equations, where the incoming field is a free field in a quasifree representation. We show that these Wightman functions that are obtained as a sum over extended Feynman graphs fulfill the basic axioms of hermiticity, invariance, spectrality (on stationary space...

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an Sp(2, R) unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural ‘generating rep...

Abstract: The invariance under unitary representations of the conformal group SL(2,R) of a quantum particle is rigorously investigated in two-dimensional spacetimes containing Killing horizons using de Alfaro-Fubini-Furlan’s model. The limit of the near-horizon approximation is considered. If the Killing horizon is bifurcate (Schwarzschild-like near horizon limit), the conformal symmetry is hid...