From Dynkin diagram symmetries to fixed point structures
From Dynkin diagram symmetries to fixed point structures
复制标题
DOI：
10.1007/bf02101182
复制
发表时间：
1995-06
影响因子：
2.4
通讯作者：
J. Fuchs;Bert Schellekens;C. Schweigert
中科院分区：
文献类型：
--
作者：
J. Fuchs;Bert Schellekens;C. Schweigert
可对称化Kac-Moody代数g的Dynkin图的任何自同构都会导出g的自同构以及g的最高权模之间的映射τω。对于一大类这样的Dynkin图自同构，我们可以用另一个Kac-Moody代数，“轨道李代数”Expense来描述这些映射的各个方面。特别地，权空间上τω的迹的生成函数，我们称之为g的“缠绕特征”（关于自同构），等于Expense的特征。无扭仿射李代数的轨道李代数与共形场论中引入的不动点理论密切相关。轨道李代数和缠绕特征标是解决共形场论中不动点归结问题的重要一步。
Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra g induces an automorphism of g and a mappingτωbetween highest weight modules of g. For a large class of such Dynkin diagram automorphisms, we can describe various aspects of these maps in terms of another Kac-Moody algebra, the “orbit Lie algebra” ğ. In particular, the generating function for the trace ofτωover weight spaces, which we call the “twining character” of g (with respect to the automorphism), is equal to a character of ğ. The orbit Lie algebras of untwisted affine Lie algebras turn out to be closely related to the fixed point theories that have been introduced in conformal field theory. Orbit Lie algebras and twining characters constitute a crucial step towards solving the fixed point resolution problem in conformal field theory.