Bourbaki

Definition 6

Tag 039D, permanent. Cite it as [Bourbaki, Tag 039D].

Théories spectrales, chapter V, § 1. Représentations unitaires

Let π\pi be an irreducible unitary representation of a topological group G in a Hilbert space E. The homomorphism χ\chi of the center C of G into U\mathbf{U} such that π(z)=χ(z)⋅1E\pi (z) =\chi (z)\cdot 1_E for all zz in C is called the central character of π\pi.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.

Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.