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Cellular bases of mirabolic Hecke algebras
Abstract
We prove that the mirabolic Hecke algebra ℋn,R(q) over a commutative ring R is cellular by constructing explicit cellular bases. When R=𝕂 is a field, we also establish a Morita equivalence between ℋn,𝕂(q) and a direct sum of Hecke algebras associated with symmetric groups. As applications, we classify the irreducible ℋn,𝕂(q)-modules and obtain a semisimplicity criterion. Finally, when 𝕂=ℂ(q), we show that the cell modules arising from one of our cellular bases coincide with Siegel's irreducible ℋn,𝕂(q)-modules.
Related
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BibTeX
@misc{chen2026cellular,
title = {{Cellular bases of mirabolic Hecke algebras}},
author = {Jian Chen and Yan Liu and Jinkui Wan and Xirui Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25268},
eprint = {2610.25268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25268},
}
RIS
TY - UNPB
TI - Cellular bases of mirabolic Hecke algebras
AU - Jian Chen
AU - Yan Liu
AU - Jinkui Wan
AU - Xirui Yu
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25268
UR - https://arxiv.org/abs/2610.25268
AB - We prove that the mirabolic Hecke algebra ℋ_n,R(q) over a commutative ring R is cellular by constructing explicit cellular bases. When R=𝕂 is a field, we also establish a Morita equivalence between ℋ_n,𝕂(q) and a direct sum of Hecke algebras associated with symmetric groups. As applications, we classify the irreducible ℋ_n,𝕂(q)-modules and obtain a semisimplicity criterion. Finally, when 𝕂=ℂ(q), we show that the cell modules arising from one of our cellular bases coincide with Siegel's irreducible ℋ_n,𝕂(q)-modules.
ER -