If $G_1 x G_2$ is a subgroup of a finite group $H$, one can restrict a representation of $H$ to $G_1 x G_2$ and examine how it decomposes. One obtains in this way a function from irreducible representations of $G_1$ to (possibly reducible, possibly zero) representations of $G_2$. In certain cases, this function turns out to be very nice. We examine a particular case of this, when the groups involved are finite groups of Lie type. A large portion of the talk will be on recalling the classification of irreducible representations of such groups due to Deligne-Lusztig and Lusztig.