decomp's People
decomp's Issues
deal with Pcgs-representation
All the functions in projs.g
assume that representations are given by maps of group generators, but this is not always the case, e.g. for soluble groups. (e.g. Sym(4) representations computed by GAP don't work with symmsquare
). Deal with this by making sure that representations are given as assumed, converting, if necessary.
more problems from irrational representations
Read("projs.g");
s4_0:=SymmetricGroup(4);
o:=
[ [ [ 1 ], [ 2 ], [ 3 ] ], [ [ 1 ], [ 2 ], [ 4 ] ], [ [ 1 ], [ 3 ], [ 4 ] ],
[ [ 2 ], [ 3 ], [ 4 ] ], [ [ 1 ], [ 2, 2 ] ],
[ [ 1 ], [ 3, 3 ] ], [ [ 1 ], [ 4, 4 ] ], [ [ 1, 1 ], [ 2 ] ], [ [ 1, 1 ], [ 3 ] ],
[ [ 1, 1 ], [ 4 ] ], [ [ 2 ], [ 3, 3 ] ], [ [ 2 ], [ 4, 4 ] ],
[ [ 2, 2 ], [ 3 ] ], [ [ 2, 2 ], [ 4 ] ], [ [ 3 ], [ 4, 4 ] ], [ [ 3, 3 ], [ 4 ] ] ];
s4:=Action(s4_0,o,OnSetsTuples);
s4p:=Group(PermutationMat(s4.1,16),PermutationMat(s4.2,16));
irrs:=IrreducibleRepresentations(s4);
ii:=List(irrs,rr->GroupHomomorphismByImages(s4,Group(Image(rr,s4.1),Image(rr,s4.2))),
[s4.1,s4.2],[Image(rr,s4.1),Image(rr,s4.2)]);
rep:=GroupHomomorphismByImages(s4,s4p,[s4.1,s4.2],[s4p.1,s4p.2]);
M:=conjmat(ii,rep);
oops, M has 18 rows, not 16; in fact, the multplicity of the 2-dim irreducible is
computed wrongly, most probably due to it not being given over Q.
if instead one does
irrs:=IrreducibleRepresentationsDixon(s4);
then things are fine, as this way all the representations are computed over Q.
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