arXiv:2610.35943v1 Announce Type: new Abstract: We prove an explicit correspondence between the irreducible finite dimensional representations of the mirabolic quantum group $MU(n)$ and those of the mirabolic Hecke algebra $MH_d$ given by the mirabolic quantum Schur-Weyl duality. In particular, this resolves a generalization of a conjecture by the second author. The proof is via a careful analysis of the $MU(n)$-weight spaces and the eigenvalues of the Jucys Murphy elements of $MH_d$ on the mirabolic tensor space.
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