Consider a restriction of an irreducible finite dimensional holomorphic representation of GL(n+1,C) to the subgroup GL(n,C). We write explicitly formulas for generators of the Lie algebra gl(n+1) in the direct sum of representations of GL(n,C). Nontrivial generators act as differential-difference operators, the differential part has order n − 1, the difference part acts on the space of parameters (highest weights) of representations. We also formulate a conjecture about unitary principal series of GL(n,C).