In a classic paper from 1990, Beilison, Lusztig and MacPherson gave a geometric realization of the quantized enveloping algebra of gl_n by defining a convolution product on the space of invariant functions over the variety of pairs of n-step partial flags over a finite field. This construction was generalized by Rosso to the mirabolic setting by modifying the points on the variety to include the additional data of a vector. A presentation for this "mirabolic quantum group" in terms of generators and relations was recently given by Fan, Zhang and Ma. I will describe this construction of the mirabolic quantum group and discuss its representation theory. Time permitting, I will also discuss a mirabolic quantum Schur-Weyl duality that this algebra satisfies with a mirabolic version of the Hecke algebra of Type A.