# Character: X3 # Comment: Weil rep # Ind: 0 # Ring: Z(w) # Sparsity: 80% # Checker result: pass # Conjugacy class representative result: pass local a, A, b, B, c, C, w, W, i, result, delta, idmat; result := rec(); w := E(3); W := E(3)^2; a := E(5)+E(5)^4; A := -1-a; # b5, b5* b := E(7)+E(7)^2+E(7)^4; B := -1-b; # b7, b7** c := E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9; C := -1-c; # b11, b11** i := E(4); result.comment := "S63 as 13 x 13 matrices\n"; result.generators := [ [[-1,0,0,0,0,0,0,0,0,0,0,0,0], [0,-1,0,0,0,0,0,0,0,0,0,0,0], [0,0,-1,0,0,0,0,0,0,0,0,0,0], [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], [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,-w,W,1,0,-2*w-W,0,1,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0], [-W,3*W,2*w+3*W,W,w,2*W,W,0,-W,2*w+W,1,-2*w-W,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [-1,1,w-W,1,W,2*w,2*w+W,0,-2*w-W,0,0,0,1]] , [[0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,-1,0,-1,0,-1,0,-1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [1,w,1,w-W,-W,-2*W,-W,-W,W,-W,W,-1,W], [-W,W,0,-1,0,-1,0,0,0,0,0,-w,0]]]; return result;