Invariant spinor representations of finite rotation matrices

Invariant representations of finite rotation matrices and some applications

The orthogonal real representations of the Poincare group

DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...

Rotations of 4nπ and the Kinematic Design of Parallel Manipulators

For parallel manipulator systems a fundamental distinction is drawn between displacement and motion. The former is a spatial relation adequately modelled by standard vector and matrix algebra. The latter is a spatial trajectory whose ‘history’ also requires modelling. Quaternion, spinor and Clifford algebra representations are utilised for this purpose specifically for rigid body finite rotatio...

QUASI-PERMUTATION REPRESENTATIONS OF SUZtTKI GROUP

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...