Tame representations of the group $\mathrm{GL}(\infty,\mathbb F_q)$

A complete classification of irreducible tame representations of the group $G(\infty)=\varinjlim G(n)$ is presented. Here $G(n)=\mathrm{GL}(n,\mathbb F_q)$ is the group of nonsingular matrices of order $n$ over the finite field $\mathbb F_q$.