| 摘要: |
| 设G=GL2(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×CBθ. 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GL2(C)全新的、无限维的不可约表示. |
| 关键词: 简约群 朴素诱导模 Bruhat分解 |
| DOI：10.3969/J.ISSN.1000-5137.2023.03.003 |
| 分类号:O186.5 |
| 基金项目: |
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| Some irreducible representations of GL2 |
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CHEN Xiaoyu, LAI Yuanxu, LI Zhize
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| Let G = GL2(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 θ of B, define the naive induced module M(θ) = CG×CBθ. In this paper, we prove that if θ is antidominant, then M(θ) is irreducible. Thus, we give a class of new infinite-dimensional irreducible representations of GL2(C). |
| Key words: reductive group naive induced module Bruhat decomposition |
