Character (Multiplicative)

A continuous Homeomorphism of a Group into the Nonzero Complex Numbers. A multiplicative character $\omega$ gives a Representation on the 1-D Space $\Bbb{C}$ of Complex Numbers, where the Representation action by $g\in G$ is multiplication by $\omega(g)$. A multiplicative character is Unitary if it has Absolute Value 1 everywhere.

References

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.