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SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
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Group: A4 RepresentationA4(2,0,0,0,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 1, 0, -1, -1) yields a state with 10 characters
Maximal nonstable state={(0, 1, 0, 1, 0), (1, 0, 0, 0, 1), (1, 1, 0, 0, 0), (0, 1, 0, 0, 1), (0, 1, 1, 0, 0), (1, 0, 1, 0, 0), (2, 0, 0, 0, 0), (0, 2, 0, 0, 0), (1, 0, 0, 1, 0), (0, 0, 2, 0, 0)}
(2) 1-PS = (1, 0, 0, 0, -1) yields a state with 11 characters
Maximal nonstable state={(0, 1, 0, 1, 0), (1, 0, 0, 0, 1), (1, 1, 0, 0, 0), (0, 1, 1, 0, 0), (1, 0, 1, 0, 0), (2, 0, 0, 0, 0), (0, 2, 0, 0, 0), (1, 0, 0, 1, 0), (0, 0, 2, 0, 0), (0, 0, 0, 2, 0), (0, 0, 1, 1, 0)}


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SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
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Group: A4 RepresentationA4(2,0,0,0,0)
Set of maximal unstable states:
(1) 1-PS = (1, 1, 1, 1, -4) yields a state with 10 characters
Maximal unstable state={(0, 1, 0, 1, 0), (1, 1, 0, 0, 0), (0, 1, 1, 0, 0), (1, 0, 1, 0, 0), (2, 0, 0, 0, 0), (0, 2, 0, 0, 0), (1, 0, 0, 1, 0), (0, 0, 2, 0, 0), (0, 0, 0, 2, 0), (0, 0, 1, 1, 0)}
(2) 1-PS = (1, 1/6, 1/6, -2/3, -2/3) yields a state with 8 characters
Maximal unstable state={(1, 0, 0, 0, 1), (1, 1, 0, 0, 0), (0, 1, 1, 0, 0), (1, 0, 1, 0, 0), (2, 0, 0, 0, 0), (0, 2, 0, 0, 0), (1, 0, 0, 1, 0), (0, 0, 2, 0, 0)}
(3) 1-PS = (1, 1, -2/3, -2/3, -2/3) yields a state with 9 characters
Maximal unstable state={(0, 1, 0, 1, 0), (1, 0, 0, 0, 1), (1, 1, 0, 0, 0), (0, 1, 0, 0, 1), (0, 1, 1, 0, 0), (2, 0, 0, 0, 0), (1, 0, 1, 0, 0), (0, 2, 0, 0, 0), (1, 0, 0, 1, 0)}


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SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
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Group: A4 RepresentationA4(2,0,0,0,0)
Set of strictly polystable states:
(1) A state with 7 characters
Strictly polystable state={(0, 1, 0, 1, 0), (0, 2, 0, 0, 0), (0, 0, 2, 0, 0), (1, 0, 0, 0, 1), (0, 0, 0, 2, 0), (0, 0, 1, 1, 0), (0, 1, 1, 0, 0)}
(2) A state with 3 characters
Strictly polystable state={(0, 0, 0, 2, 0), (0, 1, 1, 0, 0), (1, 0, 0, 0, 1)}
(3) A state with 5 characters
Strictly polystable state={(0, 1, 0, 1, 0), (1, 0, 0, 1, 0), (0, 0, 2, 0, 0), (1, 0, 0, 0, 1), (0, 1, 0, 0, 1)}