- #1
Gulli
- 96
- 0
Homework Statement
In order to construct a character table I need the character of the standard representation. The only problem is I don't know how to find the standard representation of a given group.
Homework Equations
The groupprops wiki tells me: "Take a representation of degree n obtained by the usual action of the symmetric group on the basis set of a vector space. Now, look at the n − 1-dimensional subspace of vectors whose sum of coordinates in the basis is zero. The representation restricts to an irreducible representation of degree n − 1 on this subspace. This is the standard representation." Which confuses me. What exactly does it mean to "look at the n − 1-dimensional subspace of vectors whose sum of coordinates in the basis is zero". What am I suppsoed to do here and does it mean that if I chose to represent say D3 on 96x96 matrices I get a standard representation of dimension 95 and if I choose to start out with 3x3 matrices I get a standard rep. of dimension 2?
Wikipedia and Wolfram mathworld don't even have an entry on the standard representation.
The Attempt at a Solution
I have no friggin idea... I haven't found a clear definition, nor an example to demonstrate the process.