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SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
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Group: A3 RepresentationA3(2,0,0,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 0, 0, -1) yields a state with 7 characters
Maximal nonstable state={(1, 0, 0, 1), (1, 0, 1, 0), (1, 1, 0, 0), (0, 0, 2, 0), (2, 0, 0, 0), (0, 2, 0, 0), (0, 1, 1, 0)}
(2) 1-PS = (1, 1, -1, -1) yields a state with 7 characters
Maximal nonstable state={(1, 0, 0, 1), (1, 0, 1, 0), (1, 1, 0, 0), (0, 1, 0, 1), (0, 2, 0, 0), (2, 0, 0, 0), (0, 1, 1, 0)}


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SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
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Group: A3 RepresentationA3(2,0,0,0)
Set of maximal unstable states:
(1) 1-PS = (1, 1, 1, -3) yields a state with 6 characters
Maximal unstable state={(1, 0, 1, 0), (1, 1, 0, 0), (0, 0, 2, 0), (2, 0, 0, 0), (0, 2, 0, 0), (0, 1, 1, 0)}
(2) 1-PS = (1, 1/5, -3/5, -3/5) yields a state with 5 characters
Maximal unstable state={(1, 0, 0, 1), (1, 0, 1, 0), (1, 1, 0, 0), (2, 0, 0, 0), (0, 2, 0, 0)}


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SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
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Group: A3 RepresentationA3(2,0,0,0)
Set of strictly polystable states:
(1) A state with 4 characters
Strictly polystable state={(1, 0, 0, 1), (1, 0, 1, 0), (0, 1, 0, 1), (0, 1, 1, 0)}
(2) A state with 4 characters
Strictly polystable state={(0, 2, 0, 0), (1, 0, 0, 1), (0, 0, 2, 0), (0, 1, 1, 0)}
(3) A state with 2 characters
Strictly polystable state={(1, 0, 1, 0), (0, 1, 0, 1)}