A Palm hierarchy for the decomposing measure in the problem of harmonic analysis on the infinite-dimensional unitary group, the determinantal point process with the confluent hypergeometric kernel

The main result of the paper states that, in the space of parameters of decomposing measures for the problem of harmonic analysis on the infinite-dimensional unitary group, the shift of parameter by 1 corresponds to taking the reduced Palm measure at infinity. The argument proceeds by finite-dimensional approximation of our measures by orthogonal polynomial ensembles and stems from the observation that taking the Palm measure commutes with the limit transition from finite to infinite number of particles.