Quelle ExamplesPaper.gi
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#
# These examples give all the results from Table 4 of the paper
# "Construcing Majorana Representations" - https://arxiv.org/abs/1803.10723.
#
# Where the index of a shape is given with an asterix, this implies that
# the associated representation is 3-closed
#
BindGlobal("MAJORANA_Example_S4T1", function() # Shapes 1, 3, 5*, 8
local G, T;
G := SymmetricGroup(4);
T := Filtered(AsSet(G), x -> Order(x) = 2);
return ShapesOfMajoranaRepresentation(G,T);
end );
BindGlobal("MAJORANA_Example_S4T2", function() # Shapes 1, 2, 3*
local G, T;
G := SymmetricGroup(4);
T := [ (1,2), (1,3), (1,4), (2,3), (2,4), (3,4)];;
return ShapesOfMajoranaRepresentation(G,T);
end );
BindGlobal("MAJORANA_Example_A5", function() # Shapes 1, 2, 3*, 4
local G, T;
G := AlternatingGroup(5);
T := Filtered(AsSet(G), x -> Order(x) = 2);
return ShapesOfMajoranaRepresentation(G,T);
end );
BindGlobal("MAJORANA_Example_S5", function() # Shape 1
local G, T;
G := SymmetricGroup(5);
T := Filtered(AsSet(G), x -> Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_L32", function() # Shapes 1 and 2
local G, T;
G := PSL(3,2);
T := Filtered(AsSet(G), x -> Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_A6", function() # Shapes 1, 4
local G, T;
G := AlternatingGroup(6);
T := Filtered(AsSet(G),x->Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_S6", function() # Shape 2
local G, T;
G := SymmetricGroup(6);
T := [];
Append(T, AsList(ConjugacyClass(G,(1,2))));
Append(T, AsList(ConjugacyClass(G,(1,2)(3,4))));
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_3A6",function() # Shapes 1, 2, 4
local z1, z2, G, T;
z1 := (2,6)(4,11)(7,9)(8,13)(10,14)(12,16);;
z2 := (1,2,7,4)(3,8,6,10)(5,9,13,12)(11,15)(14,17)(16,18);;
G := Group(z1,z2);;
T := Filtered(G, x -> Order(x) = 2);;
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_3S6",function() # Shape 1
local z1, z2, G, T;
z1 := (2,6)(3,5)(4,10)(8,14)(9,13)(11,17)(15,16);
z2 := (1,2,7,11,4)(3,8,15,17,10)(5,9,16,18,12);
G := Group(z1,z2);
T := [];
Append(T, AsList(ConjugacyClass(G, z1)));
Append(T, AsList(ConjugacyClass(G, (4,14)(6,10)(7,17)(11,16)(12,13)(15,18))));
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_S4S3A7", function() # Shape 8
local G, T;
G := Group((1,2),(1,2,3,4),(5,6),(5,7));;
G := Intersection(G, AlternatingGroup(7));;
T := Filtered(G, x -> Order(x) = 2);;
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_A7",function() # Shape 2
local G, T;
G := AlternatingGroup(7);
T := Filtered(AsSet(G),x->Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_S7", function() # Shape 2
local G, T;
G := SymmetricGroup(7);
T := [];
Append(T, AsList(ConjugacyClass(G,(1,2))));
Append(T, AsList(ConjugacyClass(G,(1,2)(3,4))));
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_3A7",function() # Shape 1, 2
local z1, z2, G, T;
z1 := PermList([2,4,8,1,13,15,17,10,21,3,5,25,11,28,16,6,18,7,33,27,22,9,14,35,26, 12,37,23,39,38,43,45,36,32,40,19,20,42,41,24,29,30,44,31,34]);
z2 := PermList([3,6,9,11,1,13,2,10,14,23,24,4,19,5,29,31,33,35,7,8,38,18,
28,27,36,40,12,20,26,15, 43,16,44,17,25,22,34,42,21,30,39,41,45,37,32]);
G := Group(z1,z2);
T := Filtered(G, x -> Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_3S7",function() # Shape 1
local z1, z2, G, T, C;
z1 := PermList([ 1,6,5,9,3,2,11,8,4,14,7,17,20,10,23,25,12,30,29,13,34,36,15,39,16, 42,43,28,19,18,40,46,33,21,50,22,37,44,24,31,49,26,27,38,55,32,56,48,41,35, 58,52,53,54,45,47,62,51,63,60,61,57,59]);
z2 := PermList([2,7,8,1,6,10,3,4,12,5,15,18,9,19,24,11,27,31,32,33,14,13,37,40,41, 16,20,17,43,42,22,48,45,49,21,51,25,23,36,26,52,54,34,29,28,50,30,35,55,58, 59,38,39,61,44,46,47,63,60,53,57,56,62]);
G := Group(z1,z2);
T := [];
C := ConjugacyClasses(G);
C := Filtered(C,x -> Order(Representative(x)) = 2);
C := Filtered(C,x -> Size(x) in [63, 105]);
Append(T,AsList(C[1]));
Append(T,AsList(C[2]));
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_PSL211", function() # Shape 1n
local G, T, input;
G := PSL(2,11);
T := Filtered(AsSet(G), x -> Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_L33", function() # Shape 3
local G, T;
G := PSL(3,3);
T := Filtered(G, x -> Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_M11",function() # Shape 1
local G, T;
G := MathieuGroup(11);
T := Filtered(AsSet(G), x -> Order(x) = 2);
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
BindGlobal("MAJORANA_Example_S5S3A8", function() # Shape 2*
local G,T;
G := Group((1,2),(1,2,3,4,5),(6,7),(6,8));;
G := Intersection(G, AlternatingGroup(8));;
T := Filtered(G, x -> Order(x) = 2);;
return ShapesOfMajoranaRepresentationAxiomM8(G,T);
end );
[ Dauer der Verarbeitung: 0.31 Sekunden
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2026-03-28
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