Combinatorial Models for Weyl Characters
Combinatorial Models for Weyl Characters
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Weyl 角色的组合模型
DOI：
10.1006/aima.2001.2050
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发表时间：
2002
影响因子：
1.7
通讯作者：
J. Stembridge
中科院分区：
文献类型：
--
作者：
J. Stembridge
摘要我们提出了一组公理的组合对象密切相关的柏原的晶体。我们表明，任何模型的公理，如Littelmann的路径模型，有一个字符的半单李群或代数，或更一般地说，一个对称化的卡茨-穆迪代数的不可约字符的非负和。此外，有简单的显式限制规则和规则，用于分解任何此类特征标与不可约特征标的乘积。
Abstract We present a set of axioms for combinatorial objects closely related to those for Kashiwara's crystals. We show that any model for the axioms, such as Littelmann's path model, has a character—a nonnegative sum of irreducible characters for a semisimple Lie group or algebra, or more generally, a symmetrizable Kac–Moody algebra. Moreover, there are simple explicit restriction rules and rules for decomposing the product of any such character by an irreducible character.