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.