Factor representations and their characters for the wreath products of compact groups with the infinite symmetric group
Factor representations and their characters for the wreath products of compact groups with the infinite symmetric group
复制标题
具有无穷对称群的紧群花环积的因子表示及其特征
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
T. Hirai
中科院分区：
文献类型：
--
作者：
T. Hirai
设T是紧群，G = G_∞（T）表示T与无限对称群G_∞的圈积. (1)研究了有限型图G的因子表示的第一特征标，给出了一个一般的特征标公式。(2)然后，对于每个特征标f，我们给出了对应于它的因子表示π的一个实现，其中有一个迹元v，使得f（g）=。(3)进一步研究了当n → ∞时Gn = Sn（T）的不可约特征标的极限，证明了所有的特征标都是这样得到的.
下文包含第（1）部分以及第（2）和第（3）部分的摘要。
Let T be a compact group, and denote by G = G_∞(T) the wreath product of T with the infinite symmetric group G_∞. (1) We study first characters of facter representations of finite type of G and give a general character formula. (2) Then, for each character f, we give a realization of a factor representation π corresponding to it with a trace-element v such that f(g) = . (3) Further we study limits of irreducible characters of Gn = Sn(T) as n → ∞, and show that all the characters are obtained as such limits.
The following text contains the part (1) and summaris of the parts (2) and (3).