Some Automorphisms of Generalized Kac–Moody Algebras@c
Some Automorphisms of Generalized Kac–Moody Algebras@c
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广义 Kac-Moody 代数的一些自同构@c
DOI：
10.1006/jabr.1996.6907
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发表时间：
1997
影响因子：
0.9
通讯作者：
C. Schweigert
中科院分区：
文献类型：
--
作者：
J. Fuchs;U. Ray;C. Schweigert
对于广义Kac-Moody(GKM)代数的Cartan矩阵的任何对称性，我们都联系到一族代数的自同构族，这些自同构族自然地作用于GKM代数的模。我们引入了模的缠绕特征，它是通过将这种自同构的作用插入到出现在普通特征标中的迹中而得到的。可积最高权模和Verma模的缠绕特征标满足一个涉及Weyl群的某个子群的特征标公式。这个子群被证明是另一个称为轨道李代数的GKM代数的Weyl群，因此它的孪生特征与轨道李代数的普通特征重合。
To any symmetry of the Cartan matrix of a Generalized Kac-Moody (GKM) algebra we associate a family of automorphisms of the algebra which act in a natural way on the modules of the GKM algebra. We introduce the twining character of a module which is obtained by inserting the action of such an automorphism into the trace that appears in the ordinary character. Twining characters of integrable highest weight modules and Verma modules satisfy a character formula which involves a certain subgroup of the Weyl group. This subgroup is shown to be the Weyl group of another GKM algebra, called the orbit Lie algebra, and hence the twining characters coincide with ordinary characters of the orbit Lie algebra.