A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, which resolves the problem of harmonic analysis on the infinite-dimensional unitary group

The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to taking the reduced Palm measure at infinity for the decomposing measures in question. The proof proceeds by finite-dimensional approximation of the measures by orthogonal polynomial ensembles. The key remark is that taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.