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Combinatorial description of the mirabolic quantum Schur-Weyl duality
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 MHd 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 MHd on the mirabolic tensor space.
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BibTeX
@misc{goyal2026combinatorial,
title = {{Combinatorial description of the mirabolic quantum Schur-Weyl duality}},
author = {Pallav Goyal and Daniele Rosso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35943},
eprint = {2610.35943},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35943},
}
RIS
TY - UNPB
TI - Combinatorial description of the mirabolic quantum Schur-Weyl duality
AU - Pallav Goyal
AU - Daniele Rosso
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.35943
UR - https://arxiv.org/abs/2610.35943
AB - 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.
ER -