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通过不变子群的诱导表示构造有限群的不可约表示

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  • 1. 北京大学物理学院,北京100871;2. 复旦大学 物理系,上海200438
胡嘉航(2001—),男,广东广州人,北京大学物理学院2019级本科生.

收稿日期: 2022-09-16

  修回日期: 2022-12-10

  网络出版日期: 2023-11-07

Constructing irreducible representations of a finite group using  induced representations of its invariant subgroups

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  • 1. School of Physics,Peking University,Beijing 100871,China;2. Department of Physics,Fudan University,Shanghai 200438,China

Received date: 2022-09-16

  Revised date: 2022-12-10

  Online published: 2023-11-07

摘要

本文介绍一种通过不变子群的诱导表示构造有限群所有不等价不可约表示的方法,并将其应用于第一类晶体点群特征标表的求解.该方法具有系统性和简捷性,可以作为目前教材上求点群不可约表示方法的一种补充.

本文引用格式

胡嘉航, 季峻仪, 向红军, 李新征 . 通过不变子群的诱导表示构造有限群的不可约表示[J]. 大学物理, 2023 , 42(10) : 59 . DOI: 10.16854 /j.cnki.1000-0712.220465

Abstract

This paper introduces a method of constructing all inequivalent irreducible representations of a finite group using induced representations of its invariant subgroups,and applies it to the solution of the character table of the first kind of crystal point groups. This method is systematic and simple,and can be used as a supplement to the method of solving irreducible representation of the point groups in current textbooks.


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