The crystal commutor and Drinfeld’s unitarized R-matrix
The crystal commutor and Drinfeld’s unitarized R-matrix
复制标题
晶体换向器和 Drinfeld 酉 R 矩阵
DOI：
10.1007/s10801-008-0137-0
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发表时间：
2007
影响因子：
0.8
通讯作者：
P. Tingley
中科院分区：
文献类型：
--
作者：
J. Kamnitzer;P. Tingley
摘要对于任意量子群，drinfeld定义了一个统一的r矩阵
AbstractDrinfeld defined a unitarized R-matrix for any quantum group
$U_{q}(\mathfrak {g})$
. This gives a commutor for the category of
$U_{q}(\mathfrak {g})$
representations, making it into a coboundary category. Henriques and Kamnitzer defined another commutor which also gives
$U_{q}(\mathfrak {g})$
representations the structure of a coboundary category. We show that a particular case of Henriques and Kamnitzer’s construction agrees with Drinfeld’s commutor. We then describe the action of Drinfeld’s commutor on a tensor product of two crystal bases, and explain the relation to the crystal commutor.