atlas> print_nilpotent_orbit_partitions(Sp(8)) Partition H diagram symbol Sp dim cent A(O) dual [1,1,1,1,1,1,1,1] [ 0, 0, 0, 0 ] [0,0,0,0] [[0,1,2,3,4],[1,2,3,4]] * 0 C4 [1] [9] [2,1,1,1,1,1,1] [ 1, 0, 0, 0 ] [1,0,0,0] [[1,2,3,4],[0,1,2]] 8 C3 [1,2] [7,1,1] [2,2,1,1,1,1] [ 1, 1, 0, 0 ] [0,1,0,0] [[0,1,2,4],[1,2,3]] * 14 B2+T1 [1,2] [7,1,1] [2,2,2,1,1] [ 1, 1, 1, 0 ] [0,0,1,0] [[1,2,3],[0,2]] 18 2A1 [1,2] [5,3,1] [2,2,2,2] [ 1, 1, 1, 1 ] [0,0,0,2] [[0,2,3],[1,2]] * 20 2A1 [1,2] [5,3,1] [3,3,1,1] [ 2, 2, 0, 0 ] [0,2,0,0] [[0,1,3],[1,3]] * 22 2A1 [1] [5,2,2] [3,3,2] [ 2, 2, 1, 0 ] [0,1,1,0] [[1,2],[2]] * 24 A1 [1,2] [3,3,3] [4,1,1,1,1] [ 3, 1, 0, 0 ] [2,1,0,0] [[1,2,4],[0,1]] 20 B2 [1,2] [5,1,1,1,1] [4,2,1,1] [ 3, 1, 1, 0 ] [2,0,1,0] [[0,1,4],[1,2]] * 24 A1 [1,2,2,2] [5,1,1,1,1] [4,2,2] [ 3, 1, 1, 1 ] [2,0,0,2] [[1,3],[1]] * 26 T1 [1,2,2,2] [3,3,1,1,1] [4,4] [ 3, 3, 1, 1 ] [0,2,0,2] [[0,3],[2]] * 28 T1 [1,2] [3,2,2,1,1] [6,1,1] [ 5, 3, 1, 0 ] [2,2,1,0] [[1,4],[0]] 28 A1 [1,2] [3,1,1,1,1,1,1] [6,2] [ 5, 3, 1, 1 ] [2,2,0,2] [[0,4],[1]] * 30 e [1,2,2,2] [3,1,1,1,1,1,1] [8] [ 7, 5, 3, 1 ] [2,2,2,2] [[4],[]] * 32 e [1,2] [1,1,1,1,1,1,1,1,1] atlas> print_nilpotent_orbit_partitions(Sp(6)) Partition H diagram symbol Sp dim cent A(O) dual [1,1,1,1,1,1] [ 0, 0, 0 ] [0,0,0] [[0,1,2,3],[1,2,3]] * 0 C3 [1] [7] [2,1,1,1,1] [ 1, 0, 0 ] [1,0,0] [[1,2,3],[0,1]] 6 C2 [1,2] [5,1,1] [2,2,1,1] [ 1, 1, 0 ] [0,1,0] [[0,1,3],[1,2]] * 10 A1+T1 [1,2] [5,1,1] [2,2,2] [ 1, 1, 1 ] [0,0,2] [[1,2],[1]] * 12 A1 [1,2] [3,3,1] [3,3] [ 2, 2, 0 ] [0,2,0] [[0,2],[2]] * 14 A1 [1] [3,2,2] [4,1,1] [ 3, 1, 0 ] [2,1,0] [[1,3],[0]] 14 A1 [1,2] [3,1,1,1,1] [4,2] [ 3, 1, 1 ] [2,0,2] [[0,3],[1]] * 16 e [1,2,2,2] [3,1,1,1,1] [6] [ 5, 3, 1 ] [2,2,2] [[3],[]] * 18 e [1,2] [1,1,1,1,1,1,1] atlas> set G=Sp(8) Variable G: RootDatum atlas> set L=complex_Levi (G,[0,1]) Variable L: RootDatum {This is the Levi subgroup generated by simple roots 0 and 1, the GL(3) x GL(1) Levi} atlas> L Value: root datum of Lie type 'A2.T1.T1' atlas> set L=complex_Levi (G,[1,2]) Variable L: RootDatum (overriding previous instance, which had type RootDatum) atlas> L Value: root datum of Lie type 'A2.T1.T1' atlas> set L=complex_Levi (G,[2,3]) Variable L: RootDatum (overriding previous instance, which had type RootDatum) atlas> L Value: root datum of Lie type 'C2.T1.T1' atlas> set L(int p, int q)= complex_Levi(Sp(2*p+2*q), for i:p-1 do i od ## for j:q+1 from p do j od ) Redefined L: (int,int->RootDatum) {the first loop outputs [0,1,...,p-2], which is the list of p-1 simple roots of a GL(p) Levi subgroup} {the second loop outputs [p,p+1,...,p+q], which WAS MEANT TO BE the q simple roots of the Sp(2q) subgroup} {that was an error; the last p+q shouldn't be there. Should have been "for j:q from p do j od"} {the ## concatenates these two lists, giving the simple roots of the GL(p) x Sp(2q) Levi.} atlas> L(4,3) Value: root datum of Lie type 'A3.C3.T1' {The GL(4) x Sp(6) Levi of Sp(14)} atlas> set L(int p, int q)= (Sp(2*p+2*q),complex_Levi(Sp(2*p+2*q), for i:p-1 do i od ## for j:q+1 from p do j od )) Redefined L: (int,int->RootDatum,RootDatum) {Now the output is the pair (G,L), except there is still the mistake in the last loop} {In the complex_Levi function, the last p+q (which isn't a simple root number) gets ignored. But it's going to bite us in truncated induction!}} atlas> L(4,1) Value: (simply connected root datum of Lie type 'C5',root datum of Lie type 'A3.A1.T1') atlas> L(4,2) Value: (simply connected root datum of Lie type 'C6',root datum of Lie type 'A3.C2.T1') atlas> L(4,3) Value: (simply connected root datum of Lie type 'C7',root datum of Lie type 'A3.C3.T1') atlas> L(5,3) Value: (simply connected root datum of Lie type 'C8',root datum of Lie type 'A4.C3.T1') atlas> L(5,1) Value: (simply connected root datum of Lie type 'C6',root datum of Lie type 'A4.A1.T1') {Now we want to do truncated induction from W(L) to W(G) of the Springer rep for the zero orbit of L, namely sgn(L)} atlas> whattype truncate_induce_ truncate_induce_character truncate_induce_sign truncate_induce_trivial atlas> whattype truncate_induce_sign ? Overloaded instances of 'truncate_induce_sign' (CharacterTable,[int])->int atlas> set roots(int p, int q)= for i:p-1 do i od ## for j:q+1 from p do j od Added definition [3] of roots: (int,int->[int]) atlas> roots(4,2) Value: [0,1,2,4,5,6] atlas> set roots(int p, int q)= for i:p-1 do i od ## for j:q from p do j od Redefined roots: (int,int->[int]) atlas> roots(4,2) Value: [0,1,2,4,5] atlas> set f(int p, int q)=truncate_induce_sign (Sp(2*p+2*q).character_table,roots(p,q)) Added definition [3] of f: (int,int->int) atlas> f(2,1) Runtime error: index -1 out of range (0<= . <2) in matrix column selection {This is an atlas problem, not Jeff: truncate_induce_sign is now broken. We're working on it!}