############################################################################## ## ## Green functions for ## G_2(q), q power of good prime ## ## 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; greenG2good := rec( classLengths := [ [ [ 1 ], 0 ], [ [ -1, 0, 0, 0, 0, 0, 1 ], 0 ], [ [ -1, 0, 0, 0, 0, 0, 1 ], 2 ], [ [ 1/6, 0, -1/6, 0, 0, 0, -1/6, 0, 1/6 ], 2 ], [ [ 1/2, 0, -1/2, 0, 0, 0, -1/2, 0, 1/2 ], 2 ], [ [ 1/3, 0, -1/3, 0, 0, 0, -1/3, 0, 1/3 ], 2 ], [ [ 1, 0, -1, 0, 0, 0, -1, 0, 1 ], 4 ] ], table := [ [ [ [ 1, 2, 2, 2, 2, 2, 1 ], 0 ], [ [ 1, 2, 2, 1 ], 0 ], [ [ 1, 3, 2 ], 0 ], [ [ 1, 4 ], 0 ], [ [ 1, 2 ], 0 ], [ [ 1, 1 ], 0 ], [ [ 1 ], 0 ] ], [ [ [ 1, 0, 0, 0, 0, 0, -1 ], 0 ], [ [ 1, 0, 0, 1 ], 0 ], [ [ 1, -1 ], 0 ], [ [ 1, -2 ], 0 ], [ [ 1 ], 0 ], [ [ 1, 1 ], 0 ], [ [ 1 ], 0 ] ], [ [ [ 1, 0, 0, 0, 0, 0, -1 ], 0 ], [ [ 1, 0, 0, -1 ], 0 ], [ [ 1, 1 ], 0 ], [ [ 1, 2 ], 0 ], [ [ 1 ], 0 ], [ [ 1, -1 ], 0 ], [ [ 1 ], 0 ] ], [ [ [ 1, 1, -1, -2, -1, 1, 1 ], 0 ], [ [ 1, 1, -1, -1 ], 0 ], [ [ 1, 0, -1 ], 0 ], [ [ 1, -1 ], 0 ], [ [ 1, 1 ], 0 ], [ [ 1, 2 ], 0 ], [ [ 1 ], 0 ] ], [ [ [ 1, -1, -1, 2, -1, -1, 1 ], 0 ], [ [ 1, -1, -1, 1 ], 0 ], [ [ 1, 0, -1 ], 0 ], [ [ 1, 1 ], 0 ], [ [ 1, -1 ], 0 ], [ [ 1, -2 ], 0 ], [ [ 1 ], 0 ] ], [ [ [ 1, -2, 2, -2, 2, -2, 1 ], 0 ], [ [ 1, -2, 2, -1 ], 0 ], [ [ 1, -3, 2 ], 0 ], [ [ 1, -4 ], 0 ], [ [ 1, -2 ], 0 ], [ [ 1, -1 ], 0 ], [ [ 1 ], 0 ] ], [ [ [ ], 0 ], [ [ ], 0 ], [ [ ], 0 ], [ [ 1 ], 2 ], [ [ -1 ], 2 ], [ [ 1 ], 2 ], [ [ ], 0 ] ] ], name := "Green( G_2(q) ), 1 mod 6", classInfo := [ [ "A_0", 1 ], [ "A_1", 1 ], [ "~A_1", 1 ], [ "G_2(a_1)", 1 ], [ "G_2(a_1)", 2 ], [ "G_2(a_1)", 3 ], [ "G_2", 1 ] ], charInfo := [ [ "L=A_0", "A_0" ], [ "L=A_0", "A_1" ], [ "L=A_0", "~A_1" ], [ "L=A_0", "G_2" ], [ "L=A_0", "A_2" ], [ "L=A_0", "A_1 + ~A_1" ], [ "L=G_2", [ 1 ] ] ], GFOrder := [ [ 1, 0, -1, 0, 0, 0, -1, 0, 1 ], 6 ] ); tmpff(greenG2good); Unbind(tmpvari); Unbind(tmpvarj);Unbind(tmpf);Unbind(tmpff);