Crystal Base Elements of an Extremal Weight Module Fixed by a Diagram Automorphism
Crystal Base Elements of an Extremal Weight Module Fixed by a Diagram Automorphism
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DOI：
10.1007/s10468-005-0234-x
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发表时间：
2005-12
影响因子：
0.6
通讯作者：
S. Naito;Daisuke Sagaki
中科院分区：
文献类型：
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作者：
S. Naito;Daisuke Sagaki
在我们以前的工作中，我们引入了一个双射之间的元素的晶体基地的负面（分别。正的）部分的量化通用包络代数的Kac-Moody代数是固定的图自同构和元素的晶体基地的负面（分别。正）的一部分的量子化泛包络代数的轨道李代数。在本文中，我们证明了这个双射与 *-运算交换。作为这一结果的应用，我们证明了：如果的晶图是连通的，则在图自同构所固定的一个极权λ的极权模的晶基的元素与一个极权λ的极权模的晶基的元素之间存在一个典范双射.
In our previous work, we introduced a bijection between the elements of the crystal base of the negative (resp. positive) part of the quantized universal enveloping algebraof a Kac–Moody algebrathat are fixed by a diagram automorphism and the elements of the crystal base of the negative (resp. positive) part of the quantized universal enveloping algebraof the orbit Lie algebraof. In this paper, we prove that this bijection commutes with the *-operation. As an application of this result we show that there exists a canonical bijection between the elements ℬ0(λ) of the crystal base ℬ(λ) of an extremal weight module of extremal weight λ overthat are fixed by a diagram automorphism and the elements of the crystal baseof an extremal weight module of extremal weightover, if the crystal graph ofis connected.