PreprintarXiv licencearXiv
Some remarks on realizations defining diagrammatic Hecke categories
Abstract
Every diagrammatic Hecke category is constructed from a realization, which generalizes the notion of a reflection representation of a Coxeter group. Common assumptions on realizations to ensure that the resulting categories are well behaved include Demazure surjectivity and the parabolic property (for anti-spherical quotients). We show that these assumptions are in fact unnecessary. We also give a non-inductive description of the rotational scalars for unbalanced realizations, as well as a simpler criterion to check for balancedness.
Related
BibTeX
@misc{hazi2026some,
title = {{Some remarks on realizations defining diagrammatic Hecke categories}},
author = {Amit Hazi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.02187},
eprint = {2608.02187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02187},
}
RIS
TY - UNPB
TI - Some remarks on realizations defining diagrammatic Hecke categories
AU - Amit Hazi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2608.02187
UR - https://arxiv.org/abs/2608.02187
AB - Every diagrammatic Hecke category is constructed from a realization, which generalizes the notion of a reflection representation of a Coxeter group. Common assumptions on realizations to ensure that the resulting categories are well behaved include Demazure surjectivity and the parabolic property (for anti-spherical quotients). We show that these assumptions are in fact unnecessary. We also give a non-inductive description of the rotational scalars for unbalanced realizations, as well as a simpler criterion to check for balancedness.
ER -