*************************************** SOLUTION TO GIT PROBLEM: NONSTABLE LOCI *************************************** Group: A2 RepresentationA2(7,0,0) Set of maximal non-stable states: (1) 1-PS = (1, 1/5, -6/5) yields a state with 20 characters Maximal nonstable state={(2, 3, 2), (0, 7, 0), (4, 1, 2), (5, 1, 1), (1, 5, 1), (5, 0, 2), (3, 4, 0), (4, 3, 0), (4, 2, 1), (6, 1, 0), (6, 0, 1), (7, 0, 0), (4, 0, 3), (3, 3, 1), (3, 2, 2), (1, 6, 0), (2, 5, 0), (2, 4, 1), (5, 2, 0), (0, 6, 1)} (2) 1-PS = (1, 2/3, -5/3) yields a state with 21 characters Maximal nonstable state={(2, 3, 2), (0, 7, 0), (4, 1, 2), (5, 1, 1), (1, 5, 1), (5, 0, 2), (3, 4, 0), (4, 3, 0), (4, 2, 1), (6, 1, 0), (6, 0, 1), (7, 0, 0), (0, 5, 2), (3, 3, 1), (3, 2, 2), (1, 6, 0), (2, 5, 0), (2, 4, 1), (5, 2, 0), (1, 4, 2), (0, 6, 1)} (3) 1-PS = (1, -1/4, -3/4) yields a state with 17 characters Maximal nonstable state={(4, 1, 2), (5, 1, 1), (5, 0, 2), (3, 4, 0), (4, 3, 0), (4, 2, 1), (6, 1, 0), (6, 0, 1), (7, 0, 0), (4, 0, 3), (3, 3, 1), (3, 2, 2), (2, 5, 0), (2, 4, 1), (5, 2, 0), (3, 0, 4), (3, 1, 3)} (4) 1-PS = (1, 0, -1) yields a state with 20 characters Maximal nonstable state={(2, 3, 2), (0, 7, 0), (4, 1, 2), (5, 1, 1), (1, 5, 1), (5, 0, 2), (3, 4, 0), (4, 3, 0), (4, 2, 1), (6, 1, 0), (6, 0, 1), (7, 0, 0), (4, 0, 3), (3, 3, 1), (3, 2, 2), (1, 6, 0), (2, 5, 0), (2, 4, 1), (5, 2, 0), (3, 1, 3)} ************************************** SOLUTION TO GIT PROBLEM: UNSTABLE LOCI ************************************** Group: A2 RepresentationA2(7,0,0) Set of maximal unstable states: (1) 1-PS = (1, 1, -2) yields a state with 21 characters Maximal unstable state={(2, 3, 2), (4, 1, 2), (0, 7, 0), (5, 1, 1), (5, 0, 2), (3, 4, 0), (1, 5, 1), (4, 3, 0), (4, 2, 1), (6, 0, 1), (6, 1, 0), (7, 0, 0), (0, 5, 2), (3, 3, 1), (3, 2, 2), (1, 6, 0), (2, 5, 0), (2, 4, 1), (5, 2, 0), (1, 4, 2), (0, 6, 1)} (2) 1-PS = (1, -1/8, -7/8) yields a state with 17 characters Maximal unstable state={(4, 1, 2), (5, 1, 1), (5, 0, 2), (3, 4, 0), (4, 3, 0), (4, 2, 1), (6, 0, 1), (6, 1, 0), (7, 0, 0), (4, 0, 3), (3, 3, 1), (3, 2, 2), (1, 6, 0), (2, 5, 0), (2, 4, 1), (5, 2, 0), (3, 1, 3)} (3) 1-PS = (1, -2/7, -5/7) yields a state with 17 characters Maximal unstable state={(4, 1, 2), (5, 1, 1), (5, 0, 2), (3, 4, 0), (4, 3, 0), (4, 2, 1), (6, 0, 1), (6, 1, 0), (7, 0, 0), (4, 0, 3), (3, 3, 1), (3, 2, 2), (2, 5, 0), (2, 4, 1), (5, 2, 0), (3, 0, 4), (3, 1, 3)} (4) 1-PS = (1, 1/4, -5/4) yields a state with 20 characters Maximal unstable state={(2, 3, 2), (4, 1, 2), (0, 7, 0), (5, 1, 1), (5, 0, 2), (3, 4, 0), (1, 5, 1), (4, 3, 0), (4, 2, 1), (6, 0, 1), (6, 1, 0), (7, 0, 0), (4, 0, 3), (3, 3, 1), (3, 2, 2), (1, 6, 0), (2, 5, 0), (2, 4, 1), (5, 2, 0), (0, 6, 1)} ************************************************************* SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI ************************************************************* Group: A2 RepresentationA2(7,0,0) Set of strictly polystable states: (1) A state with 4 characters Strictly polystable state={(2, 3, 2), (0, 7, 0), (1, 5, 1), (3, 1, 3)}