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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?

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# More than 1 character for a conjugacy class

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