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The goal of these notes is to give a self-contained account of therepresentation theory of $GL_2$ and $SL_2$ over a finite field, and to givesome indication of how the theory works for $GL_n$ over a finite field.

Representations of $GL_2(\Fq)$ and $SL_2(\Fq)$, and some remarks about $GL_n(\Fq)$