We do a study of the real representations of the Poincare group, motivated by the following: i) the classical electromagnetic field —from which the Poincare group was originally defined— transforms as a real representation of the Poincare group; ii) the localization of complex unitary representations of the Poincare group is incompatible with causality, Poincare covariance and energy positivity...

We give a new proof of von Neumann's theorem, which states that the Schrödinger representation of the canonical commutation relations is (up to unitary equivalence) the only one, in the case of a finite number of canonical variables.

Using method of inducing, irreducible unitary representation of Cay-ley–Klein orthogonal groups were constructed. There was proved that Kirilov's method of orbits is relevant for study of the behavior of irre-ducible representations under transitions between Cayley–Klein groups.

We construct representations for braid groups Bn via actions of Bn on a determinantal ring, thus mirroring the setting of the classical representation theory for GLn. The representations that we construct fix a certain unitary form.

We prove that any irreducible unitary representation of GL(n,R) and GL(n,C) admits an equivariant linear form with respect to one of the subgroups considered by Klyachko.

An account of scientific representation in terms of partial structures and partial morphisms is further developed. It is argued that the account addresses a variety of difficulties and challenges that have recently been raised against such formal accounts of representation. This allows some useful parallels between representation in science and art to be drawn, particularly with regard to appar...

Abstract In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For holes, focus on static perturbations, which the (exact) have group structure SO(1,3). The generators consist three spatial rotations, conformal Killing vectors obeying special melodic condition. perturbation solutions form unitary (principal series) re...