ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 26 Sep 2023 02:01:02 +0200read character tablehttps://ask.sagemath.org/question/73582/read-character-table/We can get the character table for a finite group using the .character_table() method. As an example:
G = SymmetricGroup(3)
G.character_table()
Returns
[ 1 -1 1]
[ 2 0 -1]
[ 1 1 1]
which are the signed, two-dimensional and trivial irreps, respectively (see wiki page on character tables, unfortunately can't post links yet). The columns are identity, (12) and (123) conjugacy classes. As another example, for the case of G = CyclicPermutationGroup(3), the character table returns
[ 1 1 1]
[ 1 zeta3 -zeta3 - 1]
[ 1 -zeta3 - 1 zeta3]
where the columns are identity, (123) and (132) group elements. Assuming this information is generally unknown, how can I determine which columns correspond to which conjugacy classes/group elements solely based on the sagemath functionality?Mon, 25 Sep 2023 02:19:14 +0200https://ask.sagemath.org/question/73582/read-character-table/Comment by John Palmieri for <p>We can get the character table for a finite group using the .character_table() method. As an example:</p>
<pre><code>G = SymmetricGroup(3)
G.character_table()
</code></pre>
<p>Returns </p>
<pre><code>[ 1 -1 1]
[ 2 0 -1]
[ 1 1 1]
</code></pre>
<p>which are the signed, two-dimensional and trivial irreps, respectively (see wiki page on character tables, unfortunately can't post links yet). The columns are identity, (12) and (123) conjugacy classes. As another example, for the case of G = CyclicPermutationGroup(3), the character table returns</p>
<pre><code>[ 1 1 1]
[ 1 zeta3 -zeta3 - 1]
[ 1 -zeta3 - 1 zeta3]
</code></pre>
<p>where the columns are identity, (123) and (132) group elements. Assuming this information is generally unknown, how can I determine which columns correspond to which conjugacy classes/group elements solely based on the sagemath functionality?</p>
https://ask.sagemath.org/question/73582/read-character-table/?comment=73599#post-id-73599It should be more clearly documented, though.Tue, 26 Sep 2023 02:01:02 +0200https://ask.sagemath.org/question/73582/read-character-table/?comment=73599#post-id-73599Comment by ayodan for <p>We can get the character table for a finite group using the .character_table() method. As an example:</p>
<pre><code>G = SymmetricGroup(3)
G.character_table()
</code></pre>
<p>Returns </p>
<pre><code>[ 1 -1 1]
[ 2 0 -1]
[ 1 1 1]
</code></pre>
<p>which are the signed, two-dimensional and trivial irreps, respectively (see wiki page on character tables, unfortunately can't post links yet). The columns are identity, (12) and (123) conjugacy classes. As another example, for the case of G = CyclicPermutationGroup(3), the character table returns</p>
<pre><code>[ 1 1 1]
[ 1 zeta3 -zeta3 - 1]
[ 1 -zeta3 - 1 zeta3]
</code></pre>
<p>where the columns are identity, (123) and (132) group elements. Assuming this information is generally unknown, how can I determine which columns correspond to which conjugacy classes/group elements solely based on the sagemath functionality?</p>
https://ask.sagemath.org/question/73582/read-character-table/?comment=73595#post-id-73595Ok thanks!Mon, 25 Sep 2023 23:37:22 +0200https://ask.sagemath.org/question/73582/read-character-table/?comment=73595#post-id-73595Comment by John Palmieri for <p>We can get the character table for a finite group using the .character_table() method. As an example:</p>
<pre><code>G = SymmetricGroup(3)
G.character_table()
</code></pre>
<p>Returns </p>
<pre><code>[ 1 -1 1]
[ 2 0 -1]
[ 1 1 1]
</code></pre>
<p>which are the signed, two-dimensional and trivial irreps, respectively (see wiki page on character tables, unfortunately can't post links yet). The columns are identity, (12) and (123) conjugacy classes. As another example, for the case of G = CyclicPermutationGroup(3), the character table returns</p>
<pre><code>[ 1 1 1]
[ 1 zeta3 -zeta3 - 1]
[ 1 -zeta3 - 1 zeta3]
</code></pre>
<p>where the columns are identity, (123) and (132) group elements. Assuming this information is generally unknown, how can I determine which columns correspond to which conjugacy classes/group elements solely based on the sagemath functionality?</p>
https://ask.sagemath.org/question/73582/read-character-table/?comment=73583#post-id-73583I think the columns are in the order given by `G.conjugacy_classses()`. See also `G.conjugacy_classes_representatives()`, which is mentioned in the documentation for `character_table`.Mon, 25 Sep 2023 02:57:45 +0200https://ask.sagemath.org/question/73582/read-character-table/?comment=73583#post-id-73583