PreprintCC BY 4.0arXiv
Partitions of canonical bases
Abstract
We show that various partitions of the canonical basis of quantum groups constructed by Lusztig and by Kashiwara coincide. Using this partition, we show that the subset corresponding to open Richardson varieties equals to the intersection of the subsets corresponding to the Schubert cells. We also show that in type A, the weights from open Richardson varieties are saturated in the corresponding Bruhat interval polytope.
Related
- Minimal asymptotic g-adic bases from arbitrary partitions
- Noncommutative resolutions of affine Schubert varieties in type A and canonical bases
- Integrand analysis, leading singularities and canonical bases beyond polylogarithms
- Low-Weight Canonical Logical Bases from Pair-Partition Codes
- Thickening realization and positivity properties of canonical bases
BibTeX
@misc{ye2026partitions,
title = {{Partitions of canonical bases}},
author = {Jeff York Ye},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24028},
eprint = {2608.24028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24028},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Partitions of canonical bases
AU - Jeff York Ye
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.24028
UR - https://arxiv.org/abs/2608.24028
AB - We show that various partitions of the canonical basis of quantum groups constructed by Lusztig and by Kashiwara coincide. Using this partition, we show that the subset corresponding to open Richardson varieties equals to the intersection of the subsets corresponding to the Schubert cells. We also show that in type A, the weights from open Richardson varieties are saturated in the corresponding Bruhat interval polytope.
ER -