量子幂单胞上的扭转自同构与对偶典范基
量子代数
2021-05-04 v4 表示论
摘要
本文构造了量子幂单胞上的扭转自同构，它们是幂单胞上 Berenstein-Fomin-Zelevinsky 扭转自同构的量子类比。我们证明了这些量子扭转自同构保持量子幂单胞的对偶典范基。此外，我们证明了在对称情形下，量子扭转自同构由预投射代数表示的合冲函子描述。这是 Geiß-Leclerc-Schröer 描述的量子类比，且 Geiß-Leclerc-Schröer 的结果在我们的证明中至关重要。作为推论，我们证明了量子扭转自同构与量子簇单项相容。特定量子扭转自同构的 6-周期性也得到了验证。
引用
@article{arxiv.1701.02268,
title = {Twist automorphisms on quantum unipotent cells and dual canonical bases},
author = {Yoshiyuki Kimura and Hironori Oya},
journal= {arXiv preprint arXiv:1701.02268},
year = {2021}
}
备注
v3: 57 pages. Major revision. We have detailed our explanation of the classical counterpart of the De Concini-Procesi isomorphisms and the proof of Theorem 7.25. The organization of the paper has been changed. The main results are unchanged v4: 53 pages. Minor corrections. Final version