We study 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. Theorem 1.1.

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... Let C i n,m be the coefficient of t i in the S n -equivariant Kazhdan-Lusztig polynomial of U n,m , and let c i n,m := dim C i n,m be the corresponding non-equivariant coefficient.