############################################################################## ## ## Green functions for ## E_6(q), q power of good prime, adjoint group ## ## http://www.math.rwth-aachen.de/~Frank.Luebeck/chev/Green/ ## Frank.Luebeck@Math.RWTH-Aachen.de ## ## This file can be read with GAP 3 or GAP 4. # defining q if not bound and a helper function if not IsBound(SetName) then FamilyObj:=0;LaurentPolynomialByCoefficients:=0; fi; if not IsBound(q) then q := Indeterminate(Cyclotomics); if not IsBound(SetName) then q.name := "q"; else SetName(q,"q"); fi; fi; if q = Indeterminate(Cyclotomics) then if not IsBound(SetName) then tmpf:=function(cv) return Polynomial(Cyclotomics,cv[1],cv[2]);end; else tmpf := function(cv) return LaurentPolynomialByCoefficients( FamilyObj(1),cv[1],cv[2]); end; fi; else if not IsBound(SetName) then tmpf:=function(cv) return Value(Polynomial(Cyclotomics,cv[1],cv[2]),q);end; else tmpf := function(cv) return Value(LaurentPolynomialByCoefficients( FamilyObj(1),cv[1],cv[2]),q); end; fi; fi; tmpff := function(t) t.GFOrder := tmpf(t.GFOrder); t.classLengths := List(t.classLengths,tmpf); t.table := List(t.table,r-> List(r,tmpf)); end; greenE6good := rec( classLengths := [ [ [ 1 ], 0 ], [ [ -1, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1 ], 0 ], [ [ 1, 1, 1, 1, 2, 1, 1, 1, 1, -1, -1, -1, -2, -3, -2, -2, -3, -2, -1, -1, -1, 1, 1, 1, 1, 2, 1, 1, 1, 1 ], 3 ], [ [ -1, 0, -1, -1, -1, 0, -1, 0, 1, 1, 1, 2, 3, 1, 2, 2, 1, -1, 1, -1, -2, -2, -1, -3, -2, -1, -1, -1, 0, 1, 0, 1, 1, 1, 0, 1 ], 5 ], [ [ 1/2, 0, 1/2, 1, 1/2, 1/2, 3/2, 1/2, 0, 1, 0, -1, -1/2, -1/2, -2, -3/2, -1, -3/2, -2, -1/2, -1/2, -1, 0, 1, 0, 1/2, 3/2, 1/2, 1/2, 1, 1/2, 0, 1/2 ], 10 ], [ [ 1/2, 0, -1/2, 0, 1/2, -1/2, -1/2, 1/2, 0, -1, 0, 1, -1/2, -1/2, 1, 1/2, -1, 1/2, 1, -1/2, -1/2, 1, 0, -1, 0, 1/2, -1/2, -1/2, 1/2, 0, -1/2, 0, 1/2 ], 10 ], [ [ -1, -1, -1, -2, -2, -1, -1, -1, 1, 2, 2, 3, 5, 4, 3, 4, 3, 0, 0, 0, -3, -4, -3, -4, -5, -3, -2, -2, -1, 1, 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"L=A_0", "E_6(a_2)" ], [ "L=A_0", "D_4" ], [ "L=A_0", "A_5 + A_1" ], [ "L=A_0", "A_2 + 2A_1" ], [ "L=A_0", "E_6(a_1)" ], [ "L=A_0", "E_6" ], [ "L=A_0", "A_1" ], [ "L=A_0", "3A_1" ], [ "L=A_0", "A_3 + 2A_1" ], [ "L=A_0", "A_3" ], [ "L=A_0", "A_2 + A_1" ], [ "L=A_0", "2A_2 + A_1" ], [ "L=A_0", "A_5" ], [ "L=A_0", "D_5" ], [ "L=A_0", "A_4 + A_1" ], [ "L=A_0", "D_5(a_1)" ] ], GFOrder := [ [ 1, 0, -1, 0, 0, -1, -1, 1, 0, -1, 1, 2, -1, 0, 3, 0, -2, 1, 1, -3, -1, 2, -1, -3, 1, 1, -2, 0, 3, 0, -1, 2, 1, -1, 0, 1, -1, -1, 0, 0, -1, 0, 1 ], 36 ] ); tmpff(greenE6good); Unbind(tmpvari); Unbind(tmpvarj);Unbind(tmpf);Unbind(tmpff);