# What is the principal representation?

Question on representation theory. What is the principal representation? I would like a good clear definition. I can't find it in my book (bad index) nor can I find it on the web.

matt grime
Homework Helper
It could be one of many things. Probably it is the natural representation of whatever kind of object you care about acting on itself by left (or right) multiplication. Where did you come across the phrase if it isn't defined anywhere?

Isaacs: "Characters of degree 1 are called linear characters. In particular, the function 1G with constant value 1 on G is a linear F-character. Is is called the principal F-character"

I want to know what a principal representation is.

matt grime