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More than 1 character for a conjugacy class

  1. Dec 2, 2014 #1


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    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?
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