Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Goyal, Pallav, Rosso, Daniele
Institutions: University of Southern Denmark, Indiana University Northwest
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224128459