CENTRALIZERS OF DISTINGUISHED NILPOTENT PAIRS AND RELATED PROBLEMS
CENTRALIZERS OF DISTINGUISHED NILPOTENT PAIRS AND RELATED PROBLEMS
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特异幂幂对的中心化及相关问题
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
YU RUPERTW.T.
中科院分区：
文献类型：
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作者：
YU RUPERTW.T.
在本文中，通过建立经典简单李代数中杰出幂零对的中心化子的显式组合描述，我们在经典情况下解决了潘尤舍夫猜想，即杰出幂幂对是美妙的，以及几乎主幂幂幂对的分类问题。更准确地说，我们证明了隐匿幂零对在类型 A、B 和 C 中是美妙的，但它们在类型 D 中并不总是美妙。此外，作为几乎主幂零对分类的推论，我们知道在简单带状情况下几乎主幂零对不存在，并且经典简单李代数中的几乎主幂零对的中心化子总是阿贝尔的。
In this paper, by establishing an explicit and combinatorial description of the centralizer of a distinguished nilpotent pair in a classical simple Lie algebra, we solve in the classical case Panyushev’s Conjecture which says that distinguished nilpotent pairs are wonderful, and the classification problem on almost principal nilpotent pairs. More precisely, we show that disinguished nilpotent pairs are wonderful in types A, B and C, but they are not always wonderful in type D. Also, as the corollary of the classification of almost principal nilpotent pairs, we have that almost principal nilpotent pairs do not exist in the simplylaced case and that the centralizer of an almost principal nilpotent pair in a classical simple Lie algebra is always abelian.