*************************************** SOLUTION TO GIT PROBLEM: NONSTABLE LOCI *************************************** Group: A2 RepresentationA2(10,0,0) Set of maximal non-stable states: (1) 1-PS = (1, 1/2, -3/2) yields a state with 37 characters Maximal nonstable state={(0, 9, 1), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (3, 7, 0), (5, 3, 2), (7, 1, 2), (4, 6, 0), (10, 0, 0), (6, 0, 4), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (8, 2, 0), (9, 1, 0), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (0, 8, 2), (6, 3, 1), (9, 0, 1), (5, 5, 0), (2, 5, 3), (1, 7, 2)} (2) 1-PS = (1, 1/3, -4/3) yields a state with 37 characters Maximal nonstable state={(0, 9, 1), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (3, 7, 0), (5, 3, 2), (7, 1, 2), (4, 6, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (8, 2, 0), (9, 1, 0), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (0, 8, 2), (6, 3, 1), (9, 0, 1), (5, 5, 0), (1, 7, 2)} (3) 1-PS = (1, -1/4, -3/4) yields a state with 31 characters Maximal nonstable state={(5, 2, 3), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (5, 3, 2), (3, 7, 0), (7, 1, 2), (7, 2, 1), (4, 6, 0), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (3, 6, 1), (3, 5, 2), (2, 8, 0), (6, 3, 1), (9, 0, 1), (5, 5, 0), (5, 0, 5), (8, 2, 0), (4, 1, 5), (9, 1, 0), (4, 2, 4)} (4) 1-PS = (1, 0, -1) yields a state with 36 characters Maximal nonstable state={(6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (5, 3, 2), (3, 7, 0), (7, 1, 2), (4, 6, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (5, 0, 5), (8, 2, 0), (9, 1, 0), (4, 2, 4), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (6, 3, 1), (9, 0, 1), (5, 5, 0)} (5) 1-PS = (1, 3/4, -7/4) yields a state with 38 characters Maximal nonstable state={(0, 9, 1), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (3, 7, 0), (5, 3, 2), (7, 1, 2), (4, 6, 0), (10, 0, 0), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (8, 2, 0), (9, 1, 0), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (1, 6, 3), (0, 8, 2), (6, 3, 1), (0, 7, 3), (9, 0, 1), (5, 5, 0), (2, 5, 3), (1, 7, 2)} (6) 1-PS = (1, -1/3, -2/3) yields a state with 31 characters Maximal nonstable state={(5, 2, 3), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (5, 3, 2), (3, 7, 0), (7, 1, 2), (7, 2, 1), (4, 6, 0), (8, 1, 1), (8, 0, 2), (4, 0, 6), (6, 4, 0), (7, 3, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (3, 6, 1), (3, 5, 2), (6, 3, 1), (9, 0, 1), (5, 5, 0), (5, 0, 5), (8, 2, 0), (4, 1, 5), (9, 1, 0), (4, 2, 4)} ************************************** SOLUTION TO GIT PROBLEM: UNSTABLE LOCI ************************************** Group: A2 RepresentationA2(10,0,0) Set of maximal unstable states: (1) 1-PS = (1, -2/7, -5/7) yields a state with 30 characters Maximal unstable state={(5, 2, 3), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (5, 3, 2), (3, 7, 0), (7, 1, 2), (4, 6, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (3, 6, 1), (3, 5, 2), (6, 3, 1), (9, 0, 1), (5, 5, 0), (5, 0, 5), (8, 2, 0), (4, 1, 5), (9, 1, 0), (4, 2, 4)} (2) 1-PS = (1, -1/14, -13/14) yields a state with 32 characters Maximal unstable state={(6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (5, 3, 2), (3, 7, 0), (7, 1, 2), (4, 6, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (5, 0, 5), (8, 2, 0), (9, 1, 0), (4, 2, 4), (5, 2, 3), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (6, 3, 1), (9, 0, 1), (5, 5, 0)} (3) 1-PS = (1, -4/11, -7/11) yields a state with 30 characters Maximal unstable state={(5, 2, 3), (6, 2, 2), (6, 1, 3), (4, 5, 1), (7, 0, 3), (5, 4, 1), (5, 3, 2), (3, 7, 0), (7, 1, 2), (4, 6, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (4, 0, 6), (6, 4, 0), (7, 3, 0), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (3, 6, 1), (6, 3, 1), (9, 0, 1), (5, 5, 0), (5, 0, 5), (8, 2, 0), (4, 1, 5), (9, 1, 0), (4, 2, 4)} (4) 1-PS = (1, 1, -2) yields a state with 38 characters Maximal unstable state={(0, 9, 1), (6, 1, 3), (4, 5, 1), (7, 0, 3), (6, 2, 2), (5, 4, 1), (3, 7, 0), (5, 3, 2), (4, 6, 0), (7, 1, 2), (10, 0, 0), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (8, 2, 0), (9, 1, 0), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (1, 6, 3), (0, 8, 2), (6, 3, 1), (0, 7, 3), (9, 0, 1), (5, 5, 0), (2, 5, 3), (1, 7, 2)} (5) 1-PS = (1, 2/5, -7/5) yields a state with 36 characters Maximal unstable state={(0, 9, 1), (6, 1, 3), (4, 5, 1), (7, 0, 3), (6, 2, 2), (5, 4, 1), (3, 7, 0), (5, 3, 2), (4, 6, 0), (7, 1, 2), (10, 0, 0), (6, 0, 4), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (8, 2, 0), (9, 1, 0), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (0, 8, 2), (6, 3, 1), (9, 0, 1), (5, 5, 0), (1, 7, 2)} (6) 1-PS = (1, 1/4, -5/4) yields a state with 36 characters Maximal unstable state={(0, 9, 1), (6, 1, 3), (4, 5, 1), (7, 0, 3), (6, 2, 2), (5, 4, 1), (3, 7, 0), (5, 3, 2), (4, 6, 0), (7, 1, 2), (10, 0, 0), (5, 1, 4), (6, 0, 4), (4, 4, 2), (4, 3, 3), (2, 7, 1), (3, 6, 1), (3, 5, 2), (1, 9, 0), (2, 8, 0), (8, 2, 0), (9, 1, 0), (3, 4, 3), (1, 8, 1), (5, 2, 3), (2, 6, 2), (0, 10, 0), (7, 2, 1), (8, 1, 1), (8, 0, 2), (6, 4, 0), (7, 3, 0), (6, 3, 1), (9, 0, 1), (5, 5, 0), (1, 7, 2)} ************************************************************* SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI ************************************************************* Group: A2 RepresentationA2(10,0,0) Set of strictly polystable states: (1) A state with 2 characters Strictly polystable state={(3, 5, 2), (4, 0, 6)} (2) A state with 2 characters Strictly polystable state={(0, 8, 2), (5, 1, 4)} (3) A state with 6 characters Strictly polystable state={(3, 4, 3), (1, 8, 1), (2, 6, 2), (0, 10, 0), (5, 0, 5), (4, 2, 4)}