  We introduce $q$-analogues of uniform matroids, which we call $q$-niform
matroids. While uniform matroids admit actions of symmetric groups, $q$-niform
matroids admit actions of finite general linear groups. We show that the
equivariant Kazhdan-Lusztig polynomial of a $q$-niform matroid is the unipotent
$q$-analogue of the equivariant Kazhdan-Lusztig polynomial of the corresponding
uniform matroid, thus providing evidence for the positivity conjecture for
equivariant Kazhdan-Lusztig polynomials.
