"Source: Text/RepThy/LieReps.text";
"Line: 2638";
"Date: Fri Sep 26 12:10:12 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/RepThy/LieReps.text, line: 2638
// Example: H114E23 ()
print "Example: H114E23";
ei := GetEchoInput();
SetEchoInput(true);
Q := IrreducibleSimpleSubalgebrasOfSU(2^10);
t := IrreducibleSimpleSubalgebraTreeSU(Q, 12);
assert #Vertices(t) eq 4;
t;
r := VertexLabel(t, 1); r`algebra;
assert r`algebra eq "A11";
assert r`type eq 0;
r := VertexLabel(t, 2); r;
assert r`algebra eq "C6";
[ Matrix(w) : w in r`weights ];
RepresentationDimension(RootDatum("C6"),[1,0,0,0,0,0]); 
assert $1 eq 12;
r := VertexLabel(t, 3); r`algebra;
assert r`algebra eq "A1";
[ Matrix(w) : w in r`weights ];
RepresentationDimension(RootDatum("A1"),[11]);
assert $1 eq 12;
r := VertexLabel(t, 4); r`algebra;
assert $1 eq "D6";
V := RSpace(Integers(), 6);
[ RepresentationDimension(RootDatum("C6"), v) : v in Basis(V) ];
assert $1 eq [ 12, 65, 208, 429, 572, 429 ];
[ i : i in [2..2^10] | exists{r : r in VertexLabels(
   IrreducibleSimpleSubalgebraTreeSU(Q, i)) | r`algebra eq "C6"} ];
assert $1 eq [ 12, 65, 78, 208, 364, 429, 560, 572 ];
t := IrreducibleSimpleSubalgebraTreeSU(Q, 78);
l := VertexLabels(t);
[ r`algebra : r in l ];
r := l[6];
assert r`algebra eq "C6";
[ Matrix(x) : x in r`weights ];
assert $1[1] eq 2*V.1;
SetEchoInput(ei);
