The one-dimensional representation of a group $G$ that maps each element of $G$ to the number 1. More generally, the unit representation of a group $G$ in a vector space $E$ is the representation of $G$ that maps each element of $G$ to the identity operator in $E$. The unit representation is sometimes also called the trivial representation.
Trivial representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Trivial_representation&oldid=39846