  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 the taking of the reduced
Palm measure at infinity for our decomposing measures. The proof proceeds by
finite-dimensional approximation of our measures by orthogonal polynomial
ensembles. The key remark is that the taking the reduced Palm measure commutes
with the scaling limit transition from finite to infinite particle systems.
