HALF POTENTIAL ON GEOMETRIC CRYSTALS AND CONNECTEDNESS OF CELLULAR CRYSTALS
HALF POTENTIAL ON GEOMETRIC CRYSTALS AND CONNECTEDNESS OF CELLULAR CRYSTALS
复制标题
几何晶体的半势和细胞晶体的连通性
DOI：
10.1007/s00031-022-09788-8
复制
发表时间：
2022
影响因子：
0.7
通讯作者：
NAKASHIMA TOSHIKI
中科院分区：
文献类型：
--
作者：
KANAKUBO YUKI;NAKASHIMA TOSHIKI
For any simply connected, simple complex algebraic group, we define upper/lower half-decorated geometric crystals and show that their tropicalization will be upper/lower normal Kashiwara's crystals. In particular, we show that the tropicalization of the half-decorated geometric crystal on the big Bruhat cell \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(=B{\overline{w}}_0:= {B}^{-}\cap U{\overline{w}}_0U\right) $$\end{document} is isomorphic to the Langlands dual crystalB(∞) of the nilpotent-half subalgebra of quantum group. As an application, we shall show that any cellular crystal associated with a reduced word is connected in the sense of a crystal graph.
For any simply connected, simple complex algebraic group, we define upper/lower half-decorated geometric crystals and show that their tropicalization will be upper/lower normal Kashiwara's crystals. In particular, we show that the tropicalization of the half-decorated geometric crystal on the big Bruhat cell \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(=B{\overline{w}}_0:= {B}^{-}\cap U{\overline{w}}_0U\right) $$\end{document} is isomorphic to the Langlands dual crystalB(∞) of the nilpotent-half subalgebra of quantum group. As an application, we shall show that any cellular crystal associated with a reduced word is connected in the sense of a crystal graph.
登录
查看更多内容
DOI：
10.1090/conm/248/03834
发表时间：
1999
期刊：
arXiv: Quantum Algebra
影响因子：
--
作者：
Toshiki Nakashima
通讯作者：
Toshiki Nakashima
仿射几何晶体和完美晶体的极限。
DOI：
--
发表时间：
2008
期刊：
Transactions in American Mathematical Society 30
影响因子：
--
作者：
中島俊樹;(M. Kashiwara;M. Okado)
通讯作者：
M. Okado)
DOI：
--
发表时间：
2010
期刊：
影响因子：
--
作者：
Tanisaki;T.
通讯作者：
T.
几何晶体和无能晶体
DOI：
--
发表时间：
1999
期刊：
影响因子：
--
作者：
A. Berenstein;D. Kazhdan
通讯作者：
D. Kazhdan
可集成最高重量模块的晶体底座的多面体实现
影响因子：
0.9
作者：
Toshiki Nakashima
通讯作者：
Toshiki Nakashima