On the twisted modules for finite matrix groups

Authors: KÜBRA GÜL, NURULLAH ANKARALIOĞLU

Abstract: Suppose that $W$ is an irreducible $F_{q}G$-module of dimension $n$ $% (d^{2}<n<d^{3})$ and that $H$ is given as $G=\left\langle X\right\rangle $ acting irreducibly on $W$ where $X$ is a set of $n\times n$ matrices with entries in $F=F_{q}$. In this paper, we present a Las Vegas algorithm that constructs a representation of $G$ of dimension $d$. We consider the twisted tensor products of the modules of high weights $\lambda _{1},\lambda _{2},\lambda _{d-2},\lambda _{d-1},2\lambda _{1},2\lambda _{d-1}$.

Keywords: Twisted module, irreducible $F_{q}G$-module, Las Vegas algorithm

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