I was wondering where can one find the matrices (and not just the character tables) of the irreducible representations of the most common groups (alternating, symmetric, octahedral, etc..) ?
Thanks for your help....
I was wondering where can one find the matrices (and not just the character tables) of the irreducible representations of the most common groups (alternating, symmetric, octahedral, etc..) ?
Thanks for your help....
Some remarks on how to find matrices if you are fluent with MAGMA or GAP or some such (rather than where to find them):
There's a little book called Group Tables, by Thomas and Wood, that has this information up to order 40 or so (excluding order 32).
EDIT: See also Simon Jon Nickerson, An atlas of characteristic zero representations, http://www.maths.qmw.ac.uk/~raw/SJNphd.pdf Also, you can get representations of many groups from http://brauer.maths.qmul.ac.uk/Atlas/v3/
This is an excellent question, but it can get quite complicated, see for instance the paper of Eric Kuisch who worked on this. By the way, I still find it fascinating that in (complex/characteristic 0) representation theory you throw away most of the information (the entries) of the matrices in question, except for the trace - the character. And a famous theorem of Georg Frobenius asserts that this doesn't rise a problem - up to similarity, representations are determined by their characters! For representations over fields with characteristic $p > 0$ the situation is different.