Inequivalent sets of commuting missing label operators for the nuclear surfon model

WORKSHOP ON HIGHER SYMMETRIES IN PHYSICS 6–8 November 2008, Universidad Complutense de Madrid, Madrid, SpainWe exhibit a possible choice for the four available functionally independent labelling operators for the missing label problem associated to the reduction chain so(5) ⊃ so(3).Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations

A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems

An Elementary Derivation of the Matrix Elements of Real Irreducible Representations of so(3)

Using elementary techniques, an algorithmic procedure to construct skew-symmetric matrices realizing the real irreducible representations of so(3) is developed. We further give a simple criterion that enables one to deduce the decomposition of an arbitrary real representation R of so(3) into real irreducible components from the characteristic polynomial of an arbitrary representation matrix