Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
复制标题
将复杂经典李群的表示限制为最大秩的还原子群的年轻图解方法
DOI：
10.1016/0001-8708(90)90059-v
复制
发表时间：
1990
影响因子：
1.7
通讯作者：
I. Terada
中科院分区：
文献类型：
--
作者：
K. Koike;I. Terada
本文给出了复经典群G的表示到它们的极大秩约化子群的限制规则(仅用Young图)。主要讨论了G的不可约表示对抛物子群P的Levi子群L(P)的限制。研究由抛物线子群诱导的表示是约化群表示理论中的一个重要技巧。在复经典李群和有限维表示的情况下，我们的问题可以看作是它的倒数。对于G=GL(n，C)，众所周知，这些限制公式是以Littlewood-Richardson系数和Schur函数的形式给出的。1、(5.9)(5.10)和(5.11)]和[Ko，2.51号命题。]本文证明了类似于GL(n，a=)情形的方法也适用于其他经典群，并由此给出了“限制公式”。
In this article, we give the restriction rules (using Young diagrams only) of representations of the complex classical groups G to their reductive subgroups of maximal rank.(For the classification of these subgroups, see EB Dynkin CD].) Mainly we deal with the restriction of irreducible representations of G to the Levi subgroups L (P) of parabolic subgroups P. It is an important technique in the representation theory of reductive groups to study the representations induced from the parabolic subgroups. Our problem could be regarded as its reciprocal in the case of complex classical Lie groups and finite-dimensional representations. For G= GL (n, C), it is well known that these restriction formulas are given in terms of the Littlewood-Richardson coefficients and Schur functions.(See, for example, IG Macdonald’s book [M, Chap. 1,(5.9)(5.10), and (5.11)] and [Ko, Proposition 2.51.) In this article we show that the methods analogous to the case of GL (n, a=) are also valid for the other classical groups and, as a consequence, we give “restriction formulas”