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.Thu, 17 Oct 2013 21:05:04 +0200How do I work with the character tables of Weyl groups in Sage to compute restrictions to parabolic subgroups?https://ask.sagemath.org/question/10622/how-do-i-work-with-the-character-tables-of-weyl-groups-in-sage-to-compute-restrictions-to-parabolic-subgroups/The question is essentially what is in the title. To be more concrete, let's start with the Weyl group of type $E_6$. This contains a parabolic subgroup of type $D_5$. I know how to look at the character tables of these groups using sage: for instance
W=WeylGroup(["E",6]);
ctE6=W.character_table();
ctE6
and I can do the same thing with $D_5$, of course. Also, I can realize $D_5$ as the subgroup of $W$ generated by five of the simple reflections. The problem is that I don't know how to get Sage to tell me which elements are in the conjugacy class (for example) labelled 6b in the E6 table---all I know about this class is that it consists of elements of order 6. For my purposes, I really need to know *which* elements these are, in matrix form, so that I can restrict the characters to $D_5$ and expand the result there in terms of irreducible $D_5$ characters.Thu, 17 Oct 2013 21:05:04 +0200https://ask.sagemath.org/question/10622/how-do-i-work-with-the-character-tables-of-weyl-groups-in-sage-to-compute-restrictions-to-parabolic-subgroups/