Dynkin图序列与稳定化现象
Dynkin diagram sequences and stabilization phenomena
摘要：
我们继续研究Dynkin图序列的稳定化现象在早期的工作克莱伯和本作者。我们考虑一类更一般的序列比这早期的工作，并隔离的重量，使稳定的张量积和分支的多重性的条件。我们表明，上一篇文章的所有结果可以自然地推广到这种设置。我们还证明了不定Kac-Moody代数的支配权的偏序集的一些性质，并利用这些性质给出了稳定表示环的一个更具体的定义.最后，我们考虑了经典序列$B_n, C_n, D_n$，属于范围以外的早期工作，并制定了一些简单的条件的权重，这意味着稳定。
英文摘要：
We continue the study of stabilization phenomena for Dynkin diagram sequences initiated in the earlier work of Kleber and the present author. We consider a more general class of sequences than that of this earlier work, and isolate a condition on the weights that gives stabilization of tensor product and branching multiplicities. We show that all the results of the previous article can be naturally generalized to this setting. We also prove some properties of the partially ordered set of dominant weights of indefinite Kac-Moody algebras, and use this to give a more concrete definition of a stable representation ring. Finally, we consider the classical sequences $B_n, C_n, D_n$ that fall outside the purview of the earlier work, and work out some simple conditions on the weights which imply stabilization.
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