The coherent transport through a set of N capacitively coupled quantum dots placed in a magnetic field is considered in the limit of infinite intradot and interdot interactions. The dots are attached to separate leads. The mean field slave boson approach and the equation of motion method are used. For the full spin-orbit degenerate case the low energy behavior is characterized by an SU(2N) symmetry with entangled spin and charge correlations and a phase shift Π/2N. Application of an external magnetic field gives rise to a crossover to charge Kondo state with SU(N) symmetry. The polarization of the transmitted current does depend on the magnetic field and the current becomes almost fully polarized for large fields. The calculations are also performed for finite interdot interaction. For small values, the spin Kondo effect (SU(2)) at each of the dots is weakened with increasing interdot interactions. For large values the SU(2N) Kondo effect with lower Kondo temperature than for infinite case is observed.

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