  This paper gives a plethysm formula on the characteristic map of the induced
linear characters from the unipotent upper-triangular matrices $U_n(\mathbb
F_q)$ to $GL_n(\mathbb F_q)$, the general linear group over finite field
$\mathbb F_q$. The result turns out to be a multiple of a twisted version of
the Hall-Littlewood symmetric functions $\tilde{P}_n(Y,q)$. A recurrence
relation is also given which makes it easy to carry out the computation.
