MA3E1 Groups and representations

[GrR] M. Reid, Groups and representations. Course notes available from here.  For other books see below.

The Warwick UG Handbook entry is here. 

I provide various simple Magma routines, mainly as sanity checks on the material of the notes.
All of these run instantly in the Magma online calculator.

We don't need computer algebra for the course, which is concerned with theoretical
understanding. But when we apply the theory to substantial arguments, we may need
to do hundreds of calculations, and it is unreasonable to expect to do them by
hand with any chance of getting the right answers.

BT24   The binary tetrahedral group from 2.3 and 3.4.

BD48   The binary dihedral group BD48 from Ex. 3.9.

Character table of BT24 from 5.9

I60 as matrix group from 7.5

Triangle groups from 7.6

The matrix generators of BI120 from 7.8

Generators and relations for A_4 from Ex 7.13

Flexes of the Klein quartic and proof of Proposition 10.9.


Several Warwick lecturers have used the lecture notes by Yuri Bazlov, ed. Daan Krammer

The book Gordon James and Martin Liebeck, CUP 1993 contains an excellent and
comprehensive treatment of the subject. The only small problem from my point
of view is that they write group actions on the right (that is v,g -> vg, like a matrix
multiplying row vectors on the right) whereas I want to use functional notation g(v).