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We calculate the conductance through strongly correlated T-shaped molecularor quantum dot systems under the influence of phonons. The system is modelledby the extended Anderson-Holstein Hamiltonian. The finite-U mean-field slaveboson approach is used to study many-body effects. Phonons influence bothinterference and correlations. Depending on the dot unperturbed energy and thestrength of electron-phonon interaction the system is occupied by a differentnumber of electrons which effectively interact with each other repulsively orattractively. This leads together with the interference effects to differentspin or charge Fano-Kondo effects

Impact of electron-phonon coupling on electron transport through T-shaped arrangements of quantum dots in the Kondo regime