On the infinitesimal kernel of irreducible representations of nilpotent Lie groups
On the infinitesimal kernel of irreducible representations of nilpotent Lie groups
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幂零李群不可约表示的无穷小核
DOI：
10.24033/bsmf.2016
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发表时间：
1984
期刊：
影响因子：
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通讯作者：
N. Pedersen
中科院分区：
文献类型：
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作者：
N. Pedersen
。 — 设 G 是一个连通的、单连通的李群，具有李代数 9。对于 G 的不可约表示 n，用 ker{dn) 表示，n 的微分 dn 的核被视为 9- ^ n 的复化 Qc 的通用包络代数 l/(9c) 的表示，本文首先为 G 的每个不可约表示 TC 给出 ker 的显式公式 {dn) 表示基里洛夫理论与 n 相关的共交轨道。接下来，我们给出一种代数算法，用于查找与给定的不可约表示相关的轨道。最后我们证明了 G 的群 C*-algcbra C* (G) 相对于 C* (G) 的 *-subalgcbra C" (G) 具有广义连续迹（其含义在论文中定义），并且相应的规范组合序列是有限长度的，从而锐化了 J. Dixmier 的结果。
. — Let G be a connected, simply connected nilpotent Lie group with Lie algebra 9. For an irreducible representation n of G denote by ker{dn) the kernel of the differential dn of n considered as a representation of the universal enveloping algebra l/(9c) of the complexification Qc of 9- ^ n this paper we give first for each irreducible representation TC of G an explicit formula for ker {dn) in terms of the coadjoint orbit associated by the Kirillov theory with n. Next we give an algebraic algorithm for finding the orbit associated with a given irreducible representation. Finally we show that the group C*-algcbra C* (G) of G is with generalized continuous trace with respect to the *-subalgcbra C" (G) of C* (G) (the meaning of this is defined in the paper), and that the corresponding canonical composition series is of finite length, thus sharping a result of J. Dixmier.