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Representation theory
January-April 2015

Course description: This is a first course in representation theory. We will focus on the representation theory of finite groups in characteristic zero. The first half will cover general topics that span chapters 1, 2, 3 and 5 of the book 'Linear representations of finite groups' by Serre. In the second half, we will focus on the representation theory of the symmetric group.

Prerequisite: Algebra III. A thorough knowledge of linear algebra and group theory, in particular group actions, will be assumed.

Lectures:	Thursday 2:00 p.m. - 3:15 p.m., Friday 9:10 - 10:25 a.m.
Classroom:	Lecture Hall 2
Instructors:	Kavita Sutar-Deshpande (January, February) K.V. Subrahmanyam (March, April)
Email:	ksutar AT cmi DOT ac DOT in kvs AT cmi DOT ac DOT in
Reference books:	'Linear representations of finite groups' - Jean-Pierre Serre. 'The symmetric group: representations, combinatorial algorithms and symmetric functions' - Bruce Sagan. 'Representations and characters if groups' - Gordon James, Martin Liebeck. 'Representation theory' - Fulton, Harris
Teaching Assistant:	Shraddha Srivastava (email: shraddha AT cmi DOT ac DOT in)
Grading (TBA):	30% - Final exam 40% - Homework 30% - Midterm All grades will be uploaded on Moodle.

Course components

The course will consist of in-class lectures during all weeks of the semester.
Homework will be assigned every week (barring only exam weeks).
There will be a midterm and a final examination.

Homework

Homework will be posted on this website every Sunday night and will be due in one week (on the following Monday).
You may pick up the graded homework on Tuesdays.

Late submissions will carry penalties.
You may work alone or in groups to do your homework. Feel free to approach the instructor or TA if you have questions/doubts. In any case, you must write your own solutions.

Attendance

Attendance to classes is not required but absences will be noted. Explanation for longer absences is required.

Warning against copying/plagiarism

Please be warned that I will not tolerate any kind of plagiarism in your work. You are free to search for ideas on the internet and in books but the details and work have to be your own.

According to the Merriam-Webster OnLine Dictionary, to plagiarize means:

to steal and pass off (the ideas or words of another) as one's own
to use (another's production) without crediting the source;
to commit literary theft;
to present as new and original an idea or product derived from an existing source.

Synonyms: copying, appropriation, infringement, piracy, counterfeiting, theft, borrowing.

Please visit www.plagiarism.org for more details.

Schedule

Week	Topic
1 (05/01 - 09/01)	Introduction to representation theory of finite groups; group algebras; Maschke's theorem, Schur's lemma. Homework 1
2 (12/01 - 16/01)	Examples of representations; duals and tensor products of representations. Homework 2 Holiday on 14 January (Pongal).
3 (19/01 - 23/01)	Character theory Homework 3
4 (26/01 - 30/01)	Classes cancelled. Holiday on 26 January. Deadline for course registration - 30 January
5 (02/02 - 06/02)	Character theory (continued), restriction and induction. Homework 4
6 (09/02 - 13/02)	Normal subgroups and lifted characters, linear characters, integrality of characters. Homework 5
7 (16/02 - 20/02)	Homework 6
8 (23/02 - 28/02)	Mid-semester exams week.
9
10
11
12
13
14
15	Holiday on 14 April (Dr. Ambedkar Jayanthi). Holiday on 18 April (Good Friday).
16
17 (27/04 - 01/05)	Final exams week.

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