# F:=Rationals(); local result, l; result:= rec(); result.comment:= "2a\"M20 = 2^5:A5 as 10 x 10 monomial matrices over Z.\n\ Representation 10a.\n\ Absolutely irreducible representation.\n\ Schur Index 1.\n\ \n\ SEED:\n\ Nonzero v fixed by x and negated by y*x*y*x*y^-1*x*y^-1\n\ where = 2^5:S3.\n\ v has 2 x 10 = 20 images under G; has 10 images under G.\n\ BASIS:\n\ NSB([x,y]) with above v.\n\ \n\ Possible matrix entries are in {-1,0,1}.\n\ \n\ Average number of nonzero entries for any element of the group:\n\ 10 (exactly 10%).\n\ \n\ Entry Av/Mat %Av/Mat\n\ 0 90 90\n\ ±1 10 10\n\ 1 5 5\n\ -1 5 5\n\ "; result.symmetricforms:= []; result.antisymmetricforms:= []; result.hermitianforms:= []; result.centralizeralgebra:= []; result.generators:= List( [ [ 1,0,0,0,0,0,0,0,0,0, 0,0,1,0,0,0,0,0,0,0, 0,-1,0,0,0,0,0,0,0,0, 0,0,0,0,0,1,0,0,0,0, 0,0,0,0,1,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,1, 0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,-1,0,0] ,[ 0,1,0,0,0,0,0,0,0,0, 0,0,0,1,0,0,0,0,0,0, 0,0,0,0,1,0,0,0,0,0, 1,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0,0,1,0,0, 0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0,0,0,0,1] ], l -> List( [ 0 .. 9 ], i -> l{ [ i*10+1 .. (i+1)*10 ] } ) ); Add( result.symmetricforms, IdentityMat(10) ); Add( result.centralizeralgebra, IdentityMat(10) ); return result;