We discuss the basic principles of self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in disk geometry. The analysis is based on the cyclic symmetry and periodicity of the Coulomb interaction between particles located on several rings.As a result, a system of equations is derived, which allows us readily to determine with high accuracy the equilibrium configurations of a few hundreds charged particles. For n 200 we predict the formation of a hexagonal core and valence circular rings for the centered configurations.

On duality and negative dimensions in the theory of Lie groups and symmetric spaces J. Math. Phys. 52, 083514 (2011) On the SO(10, 2) dynamical symmetry group of the MICZ-Kepler problem in a nine-dimensional space J. Math. Phys. 52, 072101 (2011) The Weyl group of the fine grading of sl(n,) associated with tensor product of generalized Pauli matrices J. Math. Phys. 52, 042109 (2011) A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space In this paper branching rules for the reduction sp(2N) '\. sp(2N -2) Xsp(2) are found, and a new pattern for labeling vectors belonging to the base for unitary irreducible representations BUIR's is found.

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