Multiplicative Character

A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character  gives a group representation on the one-dimensional space  of complex numbers, where the group representation action by  is multiplication by . 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.