1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Show that the natural representation of S3 is a direct sum of irreps

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey everyone!

    So to elaborate the title a bit more: basically I have to show that the natural representation of [itex]S_{3}[/itex] is a direct sum of the one-dimensional irreducible representation and the two-dimensional irreducible representation of [itex]S_{3}[/itex].

    2. Relevant equations
    Im not sure if there are any...

    3. The attempt at a solution
    So I dont have any formal attempt at the solution because I dont know where to start, so some explicit help on that would be great. if you could please address the following things in particular:

    - what is a natural representation - it it just a representation in which the basis vectors are simply columns of unit length in the direction they point? like [itex]e_{1},e_{2},e_{3}[/itex] etc?

    - Is the 1-D irrep just the trivial rep?

    - what is the 2-D irrep?

    Some help would be great guys, thanks!
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Show that the natural representation of S3 is a direct sum of irreps