G=E6 simply connected split, big block dual = E6 adjoint quaternionic Cells are labelled as in output of wcells for G=E6_sc_s_12 G^v=E6_ad_c_21 (not dualblock for E6_sc_s) split quaternionic special special orbit cells dualorbit cells diagram #O_R (see below) 0 31 (C) E6 0 (LDS) 222222 1 A1 30 E6(a1) 3 222022 1 2A1 28,29 D5 1,4 220202 2 A2 21,26 E6(a3) 5,11 200202 2 A2+A1 24,25 D5(a1) 6,7 121011 A2+2A1 19,20 A4+A1 12,13 121011 A3 18,23 A4 8,14 220002 2 2A2 22,27 D4 2,9 020200 2 D4(a1) 13,14,17 D4(a1) 10,15,16 000200 3 A4 12,16 A3 19,21 120001 A4+A1 9,10,11 A2+2A1 17,18,22 001010 D4 8 2A2 23 200002 1 D5(a1) 6,7 A2+A1 24,25 110001 E6(a3) 4,5,15 A2 20,26,27 020000 3 D5 2,3 2A1 28,29 100001 E6(a1) 1 A1 30 010000 E6 0 (LFS) 0 31 (C) 000000 1 LFS = large fundamental (not discrete) series #O_R is the number of real orbits of real points of E6_ad_quaternionic. This group is connected, so this can be read off from the tables in Collingwood-McGovern. b | abcdef means a-c-d-e-f the diagram gives the simple roots at which lambda is singular example: 220202 means lambda is singular at roots 3,5 Duality of Cells E6_sc_split E6_ad_quaternionic 0 31 1 30 2 29 3 28 4 27 5 26 6 24 (or 25?A) 7 25 (or 24?A) 8 23 9 22 10 17 (or 18?A) 11 18 (or 17?A) 12 21 13 16 14 15 15 20 16 19 17 10 18 14 19 13 (or 12?B) 20 12 (or 13?B) 21 11 22 9 23 8 24 6 (or 7?B) 25 7 (or 6?B) 26 5 27 2 28 4 29 1 30 3 31 0 A/B: matching of cells is determined by the "squash" graphs, except the four cells labelled A can all be switched (simultaneously), independently the 4 cells labelled B. Every cell for E6-adjoint-quaternionic contains an A(lambda) except cell #30 ***For every even orbit, the number of cells is the number of real forms, and each cell contains an A(lambda). Therefore each (even, special) unipotent Arthur packets consist of the sum (with signs?) of the unipotent representations in a single cell. ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R E6 0 (LFS) 0 31 (C) 000000 1 Stable sum: 0 (large discrete series) %stable -d -S 1,2,3,4,5,6 -c 31 lambda is singular at simple roots: 1,2,3,4,5,6 cells:31 Parameters (living at lambda): 0 0( 0,1790): 0 0 [C+,i1,C+,i1,C+,C+] 10 1 7 2 7 10 ( *, *) ( 4, *) ( *, *) ( 3, *) ( *, *) ( *, *) Dual parameters (to those living at lambda): 1878 1878(1790, 0): 20 4 [C-,r2,C-,r2,C-,C-] 1872 1879 1875 1880 1875 1872 ( *, *) (1876, *) ( *, *) (1877, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dimension of space of stable characters: 1 Everything is stable ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R E6(a3) 4,5,15 A2 20,26,27 020000 3 Three stable sums, one for each cell: cell stable sum 4 4+820 5 18+911 15 596+1874 %stable -d -c 20 -S 1,3,4,5,6 lambda is singular at simple roots: 1,3,4,5,6 cells:20 Parameters (living at lambda): 569,1874 569(448,1298): 10 3 [rn,C-,rn,C+,rn,rn] 569 435 569 714 569 569 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,3,1,5,4,3,1,6,5,4,2,3,1 1874(981, 29): 20 4 [rn,r2,rn,rn,rn,rn] 1874 1873 1874 1874 1874 1874 ( *, *) (1798, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 1310,29 1310(1298,448): 10 1 [ic,C+,ic,C-,ic,ic] 1310 1444 1310 1165 1310 1310 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4 29( 29,981): 0 0 [ic,i1,ic,ic,ic,ic] 29 28 29 29 29 29 ( *, *) ( 79, *) ( *, *) ( *, *) ( *, *) ( *, *) Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 569,1874: 1 1 sophus-t43:split-d% stable -d -c 26 -S 1,3,4,5,6 %stable -d -c 26 -S 1,3,4,5,6 lambda is singular at simple roots: 1,3,4,5,6 cells:26 Parameters (living at lambda): 180,911 180(160,1651): 6 1 [C+,C-,C+,C+,C+,C+] 295 103 276 271 270 269 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,4,3,1,5,4,3,6,5,4,2 911(641, 967): 12 2 [C+,C-,C+,rn,C+,C+] 1127 722 1093 911 1087 1127 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,4,2,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4,2 Dual parameters (to those living at lambda): 1701,969 1701(1651,160): 14 3 [C-,C+,C-,C-,C-,C-] 1586 1777 1605 1609 1610 1611 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,3,1,5,4,2,3,1,4,5,6,5,4,2,3,1,4,3,5,4,6,5 969( 967,641): 8 2 [C-,C+,C-,ic,C-,C-] 753 1160 785 969 791 753 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,3,5,4,3,1,6,5,4,3,1 Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 180,911: 1 1 sophus-t43:split-d% stable -d -c 27 -S 1,3,4,5,6 %stable -d -c 27 -S 1,3,4,5,6 lambda is singular at simple roots: 1,3,4,5,6 cells:27 Parameters (living at lambda): 4,820 4( 4,1788): 1 1 [C+,r1,C+,C+,C+,C+] 16 4 14 13 14 16 ( *, *) ( 0, 1) ( *, *) ( *, *) ( *, *) ( *, *) 2 820(585,1054): 11 1 [C+,C-,C+,i2,C+,C+] 1014 644 996 820 996 1014 ( *, *) ( *, *) ( *, *) ( 910, 912) ( *, *) ( *, *) 2,4,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4,2 Dual parameters (to those living at lambda): 1876,1060 1876(1788, 4): 19 3 [C-,i2,C-,C-,C-,C-] 1864 1876 1866 1867 1866 1864 ( *, *) (1878,1879) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1060(1054,585): 9 3 [C-,C+,C-,r1,C-,C-] 866 1237 884 1060 884 866 ( *, *) ( *, *) ( *, *) ( 968, 970) ( *, *) ( *, *) 1,3,1,4,3,1,5,4,3,1,6,5,4,3,1 Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 4,820: 1 1 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R D4 8 2A2 23 200002 1 stable sum: 1027 %stable -d -c 23 -S 2,3,4,5 lambda is singular at simple roots: 2,3,4,5 cells:23 Parameters (living at lambda): 1027 1027(712, 851): 12 0 [C-,i1,i1,i1,i1,C-] 860 1029 1029 1028 1029 863 ( *, *) (1183, *) (1174, *) (1171, *) (1170, *) ( *, *) 1,3,4,2,5,4,3,1,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 851 851( 851,712): 8 4 [C+,r2,r2,r2,r2,C+] 1018 853 853 852 853 1015 ( *, *) ( 697, *) ( 706, *) ( 709, *) ( 710, *) ( *, *) 2,3,4,2,3,4,5,4,2,3,4,5 Dimension of space of stable characters: 1 Everything is stable ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R D4(a1) 13,14,17 D4(a1) 10,15,16 000200 3 Three stable sums, one for each cell: cell stable sum 13 499+1465 14 421+1193+1851 (not unique) 17 981+1538 (note: one extra stable sum in cell 14, for example 421+1851) sophus-t43:split-d% stable -d -c 10 -S 1,2,3,5,6 %stable -d -c 10 -S 1,2,3,5,6 lambda is singular at simple roots: 1,2,3,5,6 cells:10 Parameters (living at lambda): 981,1538 981(666, 897): 12 1 [C+,C+,i2,C-,i2,C+] 1169 1160 981 829 981 1152 ( *, *) ( *, *) (1075,1076) ( *, *) (1064,1065) ( *, *) 4,2,3,1,4,5,4,2,3,1,4,3,5,6,5,4,2,3,1,4,3,5,4 1538(906, 340): 16 2 [C+,rn,C+,C-,C+,C+] 1687 1538 1671 1408 1666 1662 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4 Dual parameters (to those living at lambda): 899,340 899( 897,666): 8 3 [C-,C-,r1,C+,r1,C-] 711 720 899 1051 899 728 ( *, *) ( *, *) ( 803, 804) ( *, *) ( 816, 817) ( *, *) 1,2,3,1,4,5,4,6,5,4,2,3,1 340( 340,906): 4 2 [C-,ic,C-,C+,C-,C-] 195 340 209 470 216 218 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,5,6,5 Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 981,1538: 1 1 sophus-t43:split-d% stable -d -c 15 -S 1,2,3,5,6 %stable -d -c 15 -S 1,2,3,5,6 lambda is singular at simple roots: 1,2,3,5,6 cells:15 Parameters (living at lambda): 421,1193,1851 421(349,1433): 8 0 [i1,i1,C+,C-,C+,i1] 419 419 557 310 555 419 ( 531, *) ( 517, *) ( *, *) ( *, *) ( *, *) ( 500, *) 4,2,3,1,4,3,5,4,3,1,6,5,4,2,3,4 1193(788, 684): 14 3 [C+,C+,rn,C-,rn,C+] 1364 1353 1193 1036 1193 1346 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 3,4,2,3,1,4,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4 1851(981, 6): 20 4 [rn,rn,rn,r2,rn,rn] 1851 1851 1851 1853 1851 1851 ( *, *) ( *, *) ( *, *) (1822, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 1461,684,6 1461(1433,349): 12 4 [r2,r2,C-,C+,C-,r2] 1459 1459 1323 1570 1327 1459 (1349, *) (1363, *) ( *, *) ( *, *) ( *, *) (1380, *) 1,2,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,6 684( 684,788): 6 1 [C-,C-,ic,C+,ic,C-] 513 522 684 847 684 535 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,4,5,6,5,4,2,3,1 6( 6,981): 0 0 [ic,ic,ic,i1,ic,ic] 6 6 6 8 6 6 ( *, *) ( *, *) ( *, *) ( 63, *) ( *, *) ( *, *) Dimension of space of stable characters: 2 Basis of stable characters expressed as sums of irreducibles 421,1193,1851: 1 0 1 0 1 0 sophus-t43:split-d% stable -d -c 16 -S 1,2,3,5,6 %stable -d -c 16 -S 1,2,3,5,6 lambda is singular at simple roots: 1,2,3,5,6 cells:16 Parameters (living at lambda): 499,1465 499(382,1361): 9 1 [C+,C+,C+,C-,C+,C+] 676 661 650 387 643 645 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,1,4,5,4,2,3,1,4,6,5,4,2,3,4 1465(882, 415): 15 1 [C+,i2,C+,C-,C+,C+] 1601 1465 1598 1321 1596 1595 ( *, *) (1539,1540) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4 Dual parameters (to those living at lambda): 1381,415 1381(1361,382): 11 3 [C-,C-,C-,C+,C-,C-] 1204 1219 1230 1493 1236 1235 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,5,4,2,3,6,5,4,2,3,1,4,3,5,6 415( 415,882): 5 3 [C-,r1,C-,C+,C-,C-] 279 415 282 559 284 285 ( *, *) ( 341, 342) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,5,6,5 Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 499,1465: 1 1 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R 2A2 22,27 D4 2,9 020200 2 Two stable sums, one for each cell: cell stable sum 22 1873 27 1540 %stable -d -c 2,9 -S 1,3,5,6 lambda is singular at simple roots: 1,3,5,6 cells:2,9 Parameters (living at lambda): 1540,1873 1540(906, 342): 16 2 [C+,r2,C+,C-,C+,C+] 1686 1539 1670 1410 1665 1663 ( *, *) (1465, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4 1873(981, 28): 20 4 [rn,r2,rn,r2,rn,rn] 1873 1874 1873 1871 1873 1873 ( *, *) (1798, *) ( *, *) (1818, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 342,28 342( 342,906): 4 2 [C-,i1,C-,C+,C-,C-] 194 341 208 472 215 219 ( *, *) ( 415, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,5,6,5 28( 28,981): 0 0 [ic,i1,ic,i1,ic,ic] 28 29 28 26 28 28 ( *, *) ( 79, *) ( *, *) ( 59, *) ( *, *) ( *, *) Dimension of space of stable characters: 2 Basis of stable characters expressed as sums of irreducibles 1540,1873: 0 1 1 0 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R A3 18,23 A4 8,14 220002 2 Two stable sums, one for each cell: cell stable sum 18 1574 23 1861 %stable -d -c 8,14 -S 3,4,5 lambda is singular at simple roots: 3,4,5 cells:8,14 Parameters (living at lambda): 1574,1861 1574(918, 304): 16 2 [C-,C-,C+,i2,C+,C-] 1401 1419 1692 1574 1692 1449 ( *, *) ( *, *) ( *, *) (1639,1644) ( *, *) ( *, *) 1,2,3,4,2,3,1,5,4,2,3,1,4,5,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1861(981, 16): 20 4 [r2,r2,rn,rn,rn,r2] 1848 1878 1861 1861 1861 1875 (1793, *) (1804, *) ( *, *) ( *, *) ( *, *) (1838, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 304,16 304( 304,918): 4 2 [C+,C+,C-,r1,C-,C+] 481 463 188 304 188 433 ( *, *) ( *, *) ( *, *) ( 240, 245) ( *, *) ( *, *) 3,4,3,5,4,3 16( 16,981): 0 0 [i1,i1,ic,ic,ic,i1] 3 33 16 16 16 30 ( 94, *) ( 85, *) ( *, *) ( *, *) ( *, *) ( 39, *) Dimension of space of stable characters: 2 Basis of stable characters expressed as sums of irreducibles 1574,1861: 0 1 1 0 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R A2 21,26 E6(a3) 5,11 200202 2 Three stable sums, one for each cell: cell stable sum 21 1171+1703 26 1503,1867 one extra in union of cells: cell stable sum 21,26 1171+1503 (for example) %stable -d -c 5,11 -S 2,3,5 Dimension of space of stable characters: 3 Basis of stable characters expressed as sums of irreducibles 1171,1503,1703,1867: -1 0 0 1 1 0 1 0 1 1 0 0 %stable -d -c 5 -S 2,3,5 cells:5 Parameters (living at lambda): 1503,1867 1503(901, 370): 16 3 [C-,C+,C+,C-,C+,C-] 1348 1635 1628 1376 1615 1369 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,1,4,5,4,2,3,1,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1867(981, 22): 20 4 [r2,rn,rn,r2,rn,r2] 1876 1867 1867 1863 1867 1857 (1791, *) ( *, *) ( *, *) (1816, *) ( *, *) (1840, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 370,22 370( 370,901): 4 1 [C+,C-,C-,C+,C-,C+] 537 236 249 505 256 518 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,4,5,4,2,3 22( 22,981): 0 0 [i1,ic,ic,i1,ic,i1] 31 22 22 18 22 12 ( 92, *) ( *, *) ( *, *) ( 57, *) ( *, *) ( 41, *) Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 1503,1867: 1 1 %stable -d -c 11 -S 2,3,5 lambda is singular at simple roots: 2,3,5 cells:11 Parameters (living at lambda): 1171,1703 1171(769, 709): 13 1 [C-,C+,C+,r1,C+,C-] 984 1336 1330 1171 1327 1007 ( *, *) ( *, *) ( *, *) (1027,1028) ( *, *) ( *, *) 1,3,4,2,3,5,4,3,1,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1703(958, 177): 17 1 [C-,i2,i2,C-,i2,C-] 1595 1703 1703 1604 1703 1601 ( *, *) (1776,1778) (1771,1772) ( *, *) (1767,1769) ( *, *) 1,3,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 709,177 709( 709,769): 7 3 [C+,C-,C-,i2,C-,C+] 896 544 550 709 553 872 ( *, *) ( *, *) ( *, *) ( 851, 852) ( *, *) ( *, *) 2,3,4,2,3,5,4,2,3,4,5 177( 177,958): 3 3 [C+,r1,r1,C+,r1,C+] 285 177 177 276 177 279 ( *, *) ( 102, 104) ( 109, 110) ( *, *) ( 111, 113) ( *, *) 2,3,5 Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 1171,1703: 1 1 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R 2A1 28,29 D5 1,4 220202 2 Two stable sums, one for each cell: cell stable sum 28 1878 20 1778 %scalar -d -c 1,4 -S 3,5 lambda is singular at simple roots: 3,5 cells:1,4 Parameters (living at lambda): 1778,1878 1778(972, 104): 18 2 [C-,r2,i2,C-,i2,C-] 1663 1776 1778 1693 1778 1686 ( *, *) (1703, *) (1833,1834) ( *, *) (1809,1811) ( *, *) 1,2,3,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 1878(981, 33): 20 4 [r2,r2,rn,r2,rn,r2] 1869 1861 1878 1859 1878 1864 (1788, *) (1804, *) ( *, *) (1824, *) ( *, *) (1841, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 104,33 104( 104,972): 2 2 [C+,i1,r1,C+,r1,C+] 219 102 104 189 104 194 ( *, *) ( 177, *) ( 54, 55) ( *, *) ( 70, 72) ( *, *) 3,5 33( 33,981): 0 0 [i1,i1,ic,i1,ic,i1] 24 16 33 14 33 19 ( 89, *) ( 85, *) ( *, *) ( 65, *) ( *, *) ( 42, *) Dimension of space of stable characters: 2 Basis of stable characters expressed as sums of irreducibles 1778,1878: 0 1 1 0 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R A1 30 E6(a1) 3 222022 1 cell stable sum 30 1865 %scalar -d -c 3 -S 4 lambda is singular at simple roots: 4 cells:3 Parameters (living at lambda): 1865 1865(981, 20): 20 4 [r2,r2,r2,rn,r2,r2] 1875 1863 1846 1865 1847 1848 (1786, *) (1799, *) (1807, *) ( *, *) (1826, *) (1843, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 Dual parameters (to those living at lambda): 20 20( 20,981): 0 0 [i1,i1,i1,ic,i1,i1] 30 18 1 20 2 3 ( 87, *) ( 80, *) ( 68, *) ( *, *) ( 47, *) ( 44, *) Dimension of space of stable characters: 1 Basis of stable characters expressed as sums of irreducibles 1865: 1 ------------------------------------------------------------------- special special orbit cells dualorbit cells diagram #O_R 0 31 (C) E6 0 (LDS) 222222 1 cell stable sum 31 (trivial)