*************************************** SOLUTION TO GIT PROBLEM: NONSTABLE LOCI *************************************** Group: A2 RepresentationA2(11,0,0) Set of maximal non-stable states: (1) 1-PS = (1, 1/6, -7/6) yields a state with 42 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (8, 1, 2), (0, 10, 1), (1, 8, 2), (7, 0, 4), (7, 1, 3), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (10, 1, 0), (5, 2, 4), (3, 6, 2), (5, 3, 3), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} (2) 1-PS = (1, -2/9, -7/9) yields a state with 37 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (8, 1, 2), (5, 0, 6), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (10, 1, 0), (5, 2, 4), (3, 6, 2), (5, 3, 3), (4, 5, 2), (2, 9, 0), (3, 7, 1)} (3) 1-PS = (1, -1/3, -2/3) yields a state with 36 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (4, 2, 5), (8, 1, 2), (5, 0, 6), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (10, 1, 0), (5, 2, 4), (5, 3, 3), (4, 5, 2), (3, 7, 1)} (4) 1-PS = (1, 1/2, -3/2) yields a state with 44 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (1, 7, 3), (6, 5, 0), (0, 9, 2), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (8, 1, 2), (2, 6, 3), (0, 10, 1), (1, 8, 2), (7, 0, 4), (7, 1, 3), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (4, 4, 3), (10, 1, 0), (5, 2, 4), (3, 6, 2), (5, 3, 3), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} (5) 1-PS = (1, -3/7, -4/7) yields a state with 36 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (4, 1, 6), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (4, 0, 7), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (4, 2, 5), (8, 1, 2), (5, 0, 6), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (10, 1, 0), (5, 2, 4), (5, 3, 3), (4, 5, 2)} (6) 1-PS = (1, 2/3, -5/3) yields a state with 44 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (1, 7, 3), (6, 5, 0), (0, 9, 2), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (0, 8, 3), (8, 1, 2), (2, 6, 3), (0, 10, 1), (1, 8, 2), (7, 0, 4), (7, 1, 3), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (4, 4, 3), (10, 1, 0), (5, 3, 3), (3, 6, 2), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} (7) 1-PS = (1, 0, -1) yields a state with 42 characters Maximal nonstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (8, 1, 2), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (10, 1, 0), (5, 2, 4), (3, 6, 2), (5, 3, 3), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} ************************************** SOLUTION TO GIT PROBLEM: UNSTABLE LOCI ************************************** Group: A2 RepresentationA2(11,0,0) Set of maximal unstable states: (1) 1-PS = (1, -1/5, -4/5) yields a state with 37 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (8, 1, 2), (5, 0, 6), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (5, 3, 3), (5, 2, 4), (3, 6, 2), (10, 1, 0), (4, 5, 2), (2, 9, 0), (3, 7, 1)} (2) 1-PS = (1, -1/2, -1/2) yields a state with 36 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (4, 1, 6), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (4, 0, 7), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (4, 2, 5), (8, 1, 2), (5, 0, 6), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (5, 3, 3), (5, 2, 4), (10, 1, 0), (4, 5, 2)} (3) 1-PS = (1, -1/11, -10/11) yields a state with 38 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (8, 1, 2), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (5, 3, 3), (5, 2, 4), (3, 6, 2), (10, 1, 0), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} (4) 1-PS = (1, -4/11, -7/11) yields a state with 35 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (5, 1, 5), (8, 3, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (4, 3, 4), (4, 2, 5), (8, 1, 2), (5, 0, 6), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (5, 3, 3), (5, 2, 4), (10, 1, 0), (4, 5, 2)} (5) 1-PS = (1, 2/5, -7/5) yields a state with 43 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (0, 9, 2), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (8, 1, 2), (2, 6, 3), (0, 10, 1), (1, 8, 2), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (4, 4, 3), (5, 3, 3), (5, 2, 4), (3, 6, 2), (10, 1, 0), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} (6) 1-PS = (1, 2/11, -13/11) yields a state with 42 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (6, 5, 0), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (8, 1, 2), (0, 10, 1), (1, 8, 2), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (6, 0, 5), (4, 4, 3), (5, 3, 3), (5, 2, 4), (3, 6, 2), (10, 1, 0), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} (7) 1-PS = (1, 5/8, -13/8) yields a state with 44 characters Maximal unstable state={(6, 2, 3), (9, 2, 0), (9, 1, 1), (3, 5, 3), (8, 3, 0), (2, 7, 2), (1, 9, 1), (0, 11, 0), (9, 0, 2), (7, 4, 0), (7, 3, 1), (8, 2, 1), (1, 7, 3), (6, 5, 0), (0, 9, 2), (8, 0, 3), (7, 2, 2), (5, 6, 0), (10, 0, 1), (6, 4, 1), (0, 8, 3), (8, 1, 2), (2, 6, 3), (0, 10, 1), (1, 8, 2), (7, 1, 3), (7, 0, 4), (5, 4, 2), (6, 3, 2), (4, 7, 0), (4, 6, 1), (5, 5, 1), (3, 8, 0), (11, 0, 0), (6, 1, 4), (4, 4, 3), (5, 3, 3), (10, 1, 0), (3, 6, 2), (4, 5, 2), (2, 9, 0), (2, 8, 1), (3, 7, 1), (1, 10, 0)} ************************************************************* SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI ************************************************************* Group: A2 RepresentationA2(11,0,0) Set of strictly polystable states: (1) A state with 2 characters Strictly polystable state={(5, 2, 4), (1, 7, 3)} (2) A state with 6 characters Strictly polystable state={(5, 1, 5), (3, 5, 3), (2, 7, 2), (1, 9, 1), (4, 3, 4), (0, 11, 0)}