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!

Representation decomposition

  1. May 16, 2016 #1
    1. The problem statement, all variables and given/known data

    Show that vector representation 5 and adjoint representation 10 in SO(5) decompose respectively into representations of SO(4) as:

    541
    10
    64

    2. Relevant equations


    3. The attempt at a solution

    I understand that 5 is rep of SO(5) corresponding to Dynkin labels (1, 0). 1 is of course trivial representation. But what type of rep is 4? Once I started calculating weights I found out that Dynkin labels corresponding to (2, 0) as well as (1, 1) for SO(4) both have 4 weights (and different ones). And none of them seem to reproduce 5! Maybe there is an easier way, how would you show these decomposition?

    Weights for 5 [Dynkin (1,0) for SO(5)]:
    (1, 0), (-1, 2), (0,0), (1, -2) (0, -1)

    Weights for 4? [Dynkin (1,1) for SO(4)]:
    (1,1), (-1, 1), (1, -1), (-1, -1)

    Weights for 4? [Dynkin (3, 0) for SO(4)]:
    (3, 0), (1, 0), (-1, 0), (-3, 0)
     
  2. jcsd
  3. May 21, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Representation decomposition
  1. Spectral Decomposition (Replies: 18)

  2. A = QR Decomposition (Replies: 4)

  3. Primary Decomposition. (Replies: 0)

Loading...