PreprintCC BY 4.0arXiv
Positivity of the Mirabolic Quantum Groups
Abstract
In this paper, we construct the canonical basis for the modified mirabolic quantum sln. We then study the associated U̇v(sln)-module and U̇v(sln)-comodule structures and prove the positivity of this basis with respect to these two structures.
Related
- Combinatorial description of the mirabolic quantum Schur-Weyl duality
- Presenting mirabolic quantum Schur algebras ℳ𝒮v(2,d)
- Quantum super Schur--Weyl duality and character formulas for mirabolic Hecke algebras
- Notes on Chevalley Groups and Root Category IV: Iwasawa Decomposition and Total Positivity
- Quantum Laurent positivity in rank three
BibTeX
@misc{fan2026positivity,
title = {{Positivity of the Mirabolic Quantum Groups}},
author = {Zhaobing Fan and Haitao Ma and Zhicheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39010},
eprint = {2610.39010},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39010},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Positivity of the Mirabolic Quantum Groups
AU - Zhaobing Fan
AU - Haitao Ma
AU - Zhicheng Zhang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.39010
UR - https://arxiv.org/abs/2610.39010
AB - In this paper, we construct the canonical basis for the modified mirabolic quantum sl_n. We then study the associated U̇_v(sl_n)-module and U̇_v(sl_n)-comodule structures and prove the positivity of this basis with respect to these two structures.
ER -