A Plethysm formula on the characteristic map of induced linear characters from $U_n({\mathbb{F}}_q)$ to $G{L}_n({\mathbb{F}}_q)$

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 $G{L}_n({\mathbb{F}}_q)$, 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.