Representation theory of mirabolic quantum $\mathfrak{sl}_n$

Abstract: We show that the mirabolic quantum group $MU(n)$ is a comodule algebra over the quantized enveloping algebra $U_v(\mathfrak{sl}_n)$, and use this structure to give a complete classification of its finite dimensional representations. We also explicitly describe the correspondence between the irreducible finite dimensional representations of $MU(n)$ and the ones for the mirabolic Hecke algebra, given by the mirabolic quantum Schur-Weyl duality.