局域量子单纯坐标范畴的晶体结构
表示论
2025-09-04 v3 量子代数
摘要
与 Weyl 群元素 关联的局域量子单纯坐标范畴 是刚性单子范畴，通过对 quiver Hecke 代数的有限维graded 模块范畴的子范畴应用局域化过程获得。我们将展示 中（在grading 位移下）的简单对象的等距类族具有晶体结构，并且它等同于与 关联的细胞晶体。作为本结果的应用，我们将展示任意细胞晶体的晶体图的连通性。
引用
@article{arxiv.2502.14319,
title = {Crystal Structure of Localized Quantum Unipotent Coordinate Category},
author = {Masaki Kashiwara and Toshiki Nakashima},
journal= {arXiv preprint arXiv:2502.14319},
year = {2025}
}
备注
In v1, Proposition 6.8 is false. There is a counterexample: $\mathfrak{g}=A_3$, $i=2$, $w=s_1s_3s_2s_1s_3$. Since the paper heavily depends on this proposition, we withdraw v1. We do not know if Theorem 6.12 is true or not. In v3 with 62 pages, the error is corrected