Braid group actions on coideal subalgebras of quantized enveloping algebras
Braid group actions on coideal subalgebras of quantized enveloping algebras
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DOI：
10.1016/j.jalgebra.2011.04.001
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发表时间：
2011-02
影响因子：
0.9
通讯作者：
S. Kolb;Jacopo Pellegrini
中科院分区：
文献类型：
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作者：
S. Kolb;Jacopo Pellegrini
在量子对称对理论中出现的量子化包络代数的共理想子代数上构造辫群作用。特别地，我们构造了zn与n股经典辫群的半直积在对应于对称对(sl 2n （C), sp 2n (C)）的共理想子代数上的作用。这证明了Molev和Ragoucy的一个猜想。我们期望类似的作用存在于所有对称的简单复李代数中。给出的作用是受Lusztig在量子化包络代数上的辫群作用的启发，并在生成子上明确定义。利用计算机代数程序GAP中的包群对辫群和代数关系进行了验证。
We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of the semidirect product of Z n and the classical braid group in n strands on the coideal subalgebra corresponding to the symmetric pair (sl 2 n (C), sp 2 n (C)). This proves a conjecture by Molev and Ragoucy. We expect similar actions to exist for all symmetric simple complex Lie algebras. The given actions are inspired by Lusztigʼs braid group action on quantized enveloping algebras and are defined explicitly on generators. Braid group and algebra relations are verified with the help of the package Quagroup within the computer algebra program GAP.