## Group Representation Theory, Spring 2017

This course will cover the basic theory of representations of finite groups on complex vector spaces. The idea is that we will study groups by studying how they act on vector spaces, because linear algebra is easier than pure group theory.

There are course webpages for previous versions of this course from 2014, 2015, and 2016, containing lecture notes and problem sheets. This course will be similar, although I may rearrange some of the material.

My e-mail address is r dot bellovin at the usual Imperial College domain; feel free to e-mail me if you have questions. Office hours are Thursdays 4:30-5:30; my office is Huxley 656.

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Lectures

Lecture notes will be posted here. (updated 21/3)

The lectures are being recorded, and the videos will be posted here.

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Problem sheets

Sheet 1. Solutions to the first problem sheet.

Sheet 2. Solutions to the second problem sheet.

Sheet 3 (updated 9/2; typos corrected 19/2). Solutions to the third problem sheet.

Sheet 4 (typos corrected 6/3). Solutions to the fourth problem sheet.

Sheet 5. Solutions to the fifth problem sheet.

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Tests

There will be two progress tests, one on 16/2 and one on 14/3.
Test #1. Solutions to the first progress test (details added 24/2).

Test #2. Solutions to the second progress test.

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Mastery

The mastery question on the exam for MSc and MSci students will be on induced representations. Here is a handout on the material (updated 5/5). Some sample problems. Solutions to the sample problems.
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Class representative

The class representative is Emma McCracken; her e-mail address is emma dot mccracken14 at the usual domain name.
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Recommended books

There will not be a specific course textbook, but you may find some of the following references useful:

- G. James and M. Liebeck,
*Representations and Characters of Groups*
- J.-P. Serre,
*Linear Representations of Finite Groups*
- J. L. Alperin,
*Local Representation Theory*