Linear Representations of Finite Groups

Course title

6M018500

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

Successful students will understand complex representations of finite groups.
Successful students will be able to be able to compute characters of finite groups.
Successful students will be able to explain elementary properties of characters of finite groups.

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．	The regular representation	Read 2.4, 2.5 of the textbook.	200minutes
5．	Decomposition of a representation	Read 2.6, 2.7 of the textbook.	200minutes
6．	Subgroups, products induced representations	Read 3.1–3.3 of the textbook.	200minutes
7．	Examples	Read 5.1, 5.3 of the textbook.	200minutes
7．	Examples	Take Home Exam	240minutes
Total.	-	-	1640minutes