A continuous Homeomorphism of a Group into the Nonzero Complex Numbers. A multiplicative character gives a Representation on the 1-D Space of Complex Numbers, where the Representation action by is multiplication by . A multiplicative character is Unitary if it has Absolute Value 1 everywhere.
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.