摘要
设G=GL_(2)(C),并且B是G的标准Borel子群,并且CG,CB分别是群G和群B的在复数域C上的群代数.对于任意B的特征标θ,定义G的离散诱导模M(θ)=CG×CB^(θ).证明了当θ是反支配权时,M(θ)是个不可约表示.由此给出了一类GL_(2)(C)全新的、无限维的不可约表示.
Let G=GL_(2)(C),and let B be the standard Borel subgroup of G,and let CG(resp.CB)be the group algebra of G(resp.B)over the field of complex numbers.For any character of B,define the naive induced module M(0)=CG@cB 0.In this paper,we prove that if 3 is antidominant,then M(0)is irreducible.Thus,we give a class of new infinite-dimensional irreducible representations of GL_(2)(C).
作者
陈晓煜
赖元旭
李支泽
CHEN Xiaoyu;LAI Yuanxu;LI Zhize(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)
出处
《上海师范大学学报（自然科学版）》
2023年第3期295-302,共8页
Journal of Shanghai Normal University(Natural Sciences)
基金
Shanghai Sailing Program(17YF1413800)
The National Natural Science Foundation of China(11701373)。
关键词
简约群
朴素诱导模
Bruhat分解
reductive group
naive induced module
Bruhat decomposition
