I may have run into a bug in calculating the eigenvalues of a representation.
Here's what I was trying :
--------------------------------------------------------------------------------
gap> data := CharTable("SL",2,13);;
gap> rep := data.irreducibles[14];
[ 6, -6, E(13)+E(13)^3+E(13)^4+E(13)^9+E(13)^10+E(13)^12,
E(13)^2+E(13)^5+E(13)^6+E(13)^7+E(13)^8+E(13)^11,
-E(13)-E(13)^3-E(13)^4-E(13)^9-E(13)^10-E(13)^12,
-2*E(13)-E(13)^2-2*E(13)^3-2*E(13)^4-E(13)^5-E(13)^6-E(13)^7-E(13)^8
-2*E(13)^9-2*E(13)^10-E(13)^11-2*E(13)^12, 0, 0, 0, 0, 0, 1, -1, 1, -1,
1, -1 ]
#no problems for this class
gap> Eigenvalues(data,rep,5);
[ 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
0 ]
#this one has the problem; shouldn't the result be integers?
gap> Eigenvalues(data,rep,6);
[ 7/13, -7/13, 7/13, 6/13, 7/13, -7/13, 7/13, -7/13, 7/13, 6/13, 7/13, 6/13,
-6/13, 6/13, 7/13, 6/13, 7/13, -7/13, 7/13, -7/13, 7/13, 6/13, 7/13, -7/13,
7/13, 6/13 ]
#no problems for this class either
gap> Eigenvalues(data,rep,7);
[ 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0 ]
--------------------------------------------------------------------------------
Jacob Hirbawi
JcbHrb@CERF.net