 The infinitesimal character is the linear form on the center "Z" of the universal enveloping algebra of the Lie algebra of "G" that the representation induces.This construction relies on some extended version of Schur's lemma to show that any "z" in "Z" acts on "V" as a scalar, which by abuse of notation could be written ρ("z").In more classical language, "z" is a differential operator, constructed from the infinitesimal transformations which are induced on "V" by the Lie algebra of "G".