Character Table of S3

A brief derivation of the character table of S3, the symmetric group on three symbols. Assumes basic knowledge of groups and group representation theory.

If you have any questions please put them in the comment section and ill do my best to answer. Hope this was of some use.

Category:

Science & Technology

Tags:

• math
• maths
• mathematics
• teaching
• group
• representation
• character
• table
• S3
• D6
• symmetric
• on
• three
• symbols
• dihedral
• gro

[gauss1729]

to autumn16190:

notice that the trivial and sign representations are both 1-dimensional, and the geometric is 2-dimseional. 1-D representations are 1x1 matrices i.e. just a number, so the identity is just 1.

On the other hand, 2-D reps are 2x2 matrices. So the identity is the 2x2 identity matrix. This has trace 2 therefore the character is 2.

[autumn16190]

Why dont you mention the representations of (1)? Why is this got value 1 in the trivial and sign representations and 2 in the geometric representations?