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[en] Let M be an oriented Riemannian manifold and SO(M) its oriented orthonormal frame bundle. Assume there exists a reduction of the structure group to a subgroup G. We say that a G-structure M is minimal if P is a minimal submanifold of SO(M), where we equip SO(M) in the natural Riemannian metric. We give non-trivial examples of minimal G-structures for and having some special features—locally conformally Kähler and -Kenmotsu manifolds, respectively.
[en] A new type of Young tableaux with negative boxes is introduced. The product of two such generalized Young tableaux is defined and allows to develop an algorithm for the reduction of the product of SO(n) representation. Hereafter, a general formula for such a reduction is presented for n = 2p+1. The case n = 2p being studied in Ref. 5
[en] Supergravity has better renormalizability properties than Einstein gravitation. Explicit calculations and theoretical proofs indicate that the so-called SO(n) models are one- and two-loop finite. Nothing is yet known about three-loop properties. 31 references
[en] The connection between a three-dimensional nonrelativistic hydrogen atom with positive energy and a four-dimensional isotropic harmonic oscillator with repulsive potential is established by applying Jordan-Schwinger boson calculus to the algebra of the Laplace-Runge-Lenz-Pauli vector. The spectrum generating group SO(4,2) both for the bound and free states of the three-dimensional hydrogen atom arises as a quotient of the group Sp(8,R) associated to a four-dimensional isotropic harmonic oscillator with constraint
[en] Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation among three types of representations of G: positive energy (unitary lowest weight) representations, (holomorphic) discrete series representations and non-unitary finite-dimensional irreps. We consider mainly the conformal groups SOo(n, 2) treating in full detail the cases n = 1, 3, 4