Course title
6M0185001
Linear Representations of Finite Groups

 KAMEKO Masaki
Course content
We cover Part I of Serre's textbook "Representations and Characters", pp.3–45.
Purpose of class
This is a course on the representation theory of finite groups over the complex numbers. Representation theory is a dominant theme in mathematics. It has a significant influence on physic, chemistry, and other disciplines. The representation theory of finite groups over the complex numbers is a beautiful and relatively elementary subject. However, it also exhibits the most fundamental features of other representation theories. It also offers the computation of tractable examples.
Goals and objectives
  1. Successful students will understand complex representations of finite groups.
  2. Successful students will be able to be able to compute characters of finite groups.
  3. Successful students will be able to explain elementary properties of characters of finite groups.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 MIdterm examination Final examination Total.
1. 25% 25%
2. 25% 25%
3. 50% 50%
Total. 50% 50% -
Language
English
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Generalities on linear representations Read 1.1–1.6 of the text book. 200minutes
2． The character of a representation Read 2.1 of the textbook. 200minutes
3． Schur’s lemma, orthogonality relations Read 2.2, 2.3 of the textbook. 200minutes
4． Midterm examination and review Review lectures 1,2,3. 200minutes
5． The regular representation and decomposition of a representation Read 2.4, 2.5, 2.6, 2.7 of the textbook. 200minutes
6． Subgroups, products induced representations Read 3.1, 3.2, 3.3 of the textbook. 200minutes
7． Final examination and review Review lectures 4,5,6. 200minutes
8． N/A N/A 0minutes
9． N/A N/A 0minutes
10． N/A N/A 0minutes
11． N/A N/A 0minutes
12． N/A N/A 0minutes
13． N/A N/A 0minutes
14． N/A N/A 0minutes
Total. - - 1400minutes
Evaluation method and criteria
Midterm examination 50%, finial examination 50%. As a criterion, if the student is judged to have understood 60% of the content covered in class, the final grade will be 60.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Textbooks and reference materials
Serre's textbook "Representations and Characters"
Prerequisites
Linear Algebra, Algebra, , Group Theory (undergraduate level)
Office hours and How to contact professors for questions
  • By appointment. Send me an e-mail. kameko@shibaura-it.ac.jp
Regionally-oriented
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic interpersonal skills
  • Course that cultivates a basic self-management skills
  • Course that cultivates a basic problem-solving skills
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 1.NO POVERTY
  • 4.QUALITY EDUCATION
  • 8.DECENT WORK AND ECONOMIC GROWTH
  • 17.PARTNERSHIPS FOR THE GOALS
Last modified : Wed Mar 27 04:04:47 JST 2024