Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

More than 1 character for a conjugacy class

  1. Dec 2, 2014 #1

    ChrisVer

    User Avatar
    Gold Member

    Hi,
    I am trying to find the characters for the [itex]S_4[/itex] group, in the conjugacy class [itex]K= (..)(..)[/itex] and the two 3 dimensional and one 2 dimensional representations of the group.

    I use the relation obtained from the classes' algebra, which after some steps becomes::
    [itex] |K|^2 \chi^{\nu} (K) \chi^\nu (K) = d_\nu \Big[ 3 d_\nu + 2 |K| \chi^\nu (K) \Big] [/itex]
    after inserting the numbers ([itex]|K|=3, d=3[/itex]) I find for the two 3-dimensional the same equation, and give for those [itex]X[/itex]'s:
    [itex] X(K)^2 - 2 X(K) -3 =0 \Rightarrow X=-1, X=3[/itex]

    and for the 2-dimensional ([itex]|K|=3, d=2[/itex]), [itex]x[/itex]:
    [itex] 3 x(K)^2 - 4 x(K) -4=0 \Rightarrow X=2, X= -\frac{2}{3}[/itex]

    Obviously I'm getting the same result as the bibliography but I also get the [itex]X=3[/itex] and [itex]x= - \frac{2}{3}[/itex]... How can I discard them?
     
  2. jcsd
  3. Dec 7, 2014 #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