A Plethysm Formula on the Characteristic Map of Induced Linear Characters from $U_n(\mathbb F_q)$ to $GL(\mathbb F_q)$

Abstract

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.