- Published 2007

algebraic structures such as groups, rings, and algebras have clear definitions but often lack simple, natural representations. To get around this problem we represent these abstract structures as concrete structures which we better understand, namely in matrices. This idea motivates the study of representation theory. Example. Consider the symmetric group Sn = {σ : {1, ..., n} → {1, ..., n} | σ is a bijection}. We can represent elements of Sn as matrices with exactly one 1 in every row and column and zeros elsewhere. For example, σ = ( 1 2 3 4 5 5 4 1 3 2 ) 7→ perm(σ) = 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0

@inproceedings{2007Math1,
title={Math 156 : Representation Theory},
author={},
year={2007}
}