***************************************
SOLUTION TO GIT PROBLEM: NONSTABLE LOCI
***************************************
Group: A3 RepresentationA3(3,1,0,0)
Set of maximal non-stable states:
(1) 1-PS = (1, 1, 1, -3) yields a state with 22 characters
Maximal nonstable state={(1, 2, 1, 0), (2, 0, 2, 0), (3, 0, 1, 0), (0, 1, 2, 1), (1, 0, 2, 1), (0, 0, 3, 1), (0, 3, 0, 1), (0, 1, 3, 0), (1, 1, 1, 1), (1, 1, 2, 0), (1, 0, 3, 0), (3, 0, 0, 1), (1, 3, 0, 0), (1, 2, 0, 1), (2, 2, 0, 0), (2, 1, 1, 0), (0, 3, 1, 0), (2, 1, 0, 1), (3, 1, 0, 0), (0, 2, 1, 1), (2, 0, 1, 1), (0, 2, 2, 0)}
(2) 1-PS = (1, -1/3, -1/3, -1/3) yields a state with 19 characters
Maximal nonstable state={(1, 2, 1, 0), (2, 0, 0, 2), (2, 0, 2, 0), (1, 0, 2, 1), (1, 1, 1, 1), (1, 1, 2, 0), (1, 0, 3, 0), (3, 0, 0, 1), (1, 3, 0, 0), (1, 2, 0, 1), (2, 2, 0, 0), (2, 1, 1, 0), (2, 1, 0, 1), (1, 0, 0, 3), (1, 1, 0, 2), (1, 0, 1, 2), (3, 1, 0, 0), (2, 0, 1, 1), (3, 0, 1, 0)}
(3) 1-PS = (1, 1/3, -1/3, -1) yields a state with 18 characters
Maximal nonstable state={(1, 2, 1, 0), (2, 0, 0, 2), (2, 0, 2, 0), (0, 3, 0, 1), (1, 1, 1, 1), (1, 1, 2, 0), (1, 0, 3, 0), (3, 0, 0, 1), (1, 3, 0, 0), (1, 2, 0, 1), (2, 2, 0, 0), (2, 1, 1, 0), (0, 2, 2, 0), (0, 3, 1, 0), (2, 1, 0, 1), (3, 1, 0, 0), (2, 0, 1, 1), (3, 0, 1, 0)}
(4) 1-PS = (1, 1, -1, -1) yields a state with 20 characters
Maximal nonstable state={(1, 2, 1, 0), (2, 0, 0, 2), (2, 0, 2, 0), (3, 0, 1, 0), (0, 3, 0, 1), (0, 2, 0, 2), (1, 1, 1, 1), (1, 1, 2, 0), (3, 0, 0, 1), (1, 3, 0, 0), (1, 2, 0, 1), (2, 2, 0, 0), (2, 1, 1, 0), (0, 3, 1, 0), (2, 1, 0, 1), (1, 1, 0, 2), (3, 1, 0, 0), (0, 2, 1, 1), (2, 0, 1, 1), (0, 2, 2, 0)}
(5) 1-PS = (1, 0, 0, -1) yields a state with 19 characters
Maximal nonstable state={(1, 2, 1, 0), (2, 0, 0, 2), (2, 0, 2, 0), (3, 0, 1, 0), (1, 0, 2, 1), (0, 1, 3, 0), (1, 1, 1, 1), (1, 1, 2, 0), (1, 0, 3, 0), (3, 0, 0, 1), (1, 3, 0, 0), (1, 2, 0, 1), (2, 2, 0, 0), (2, 1, 1, 0), (0, 3, 1, 0), (2, 1, 0, 1), (3, 1, 0, 0), (2, 0, 1, 1), (0, 2, 2, 0)}


**************************************
SOLUTION TO GIT PROBLEM: UNSTABLE LOCI
**************************************
Group: A3 RepresentationA3(3,1,0,0)
Set of maximal unstable states:
(1) 1-PS = (1, 5/13, -7/13, -11/13) yields a state with 15 characters
Maximal unstable state={(1, 2, 1, 0), (2, 0, 0, 2), (2, 0, 2, 0), (2, 1, 1, 0), (0, 3, 1, 0), (0, 3, 0, 1), (2, 1, 0, 1), (3, 1, 0, 0), (1, 1, 2, 0), (3, 0, 0, 1), (1, 3, 0, 0), (2, 0, 1, 1), (3, 0, 1, 0), (1, 2, 0, 1), (2, 2, 0, 0)}
(2) 1-PS = (1, 3/19, -5/19, -17/19) yields a state with 15 characters
Maximal unstable state={(1, 2, 1, 0), (2, 0, 0, 2), (2, 0, 2, 0), (2, 1, 1, 0), (0, 3, 1, 0), (2, 1, 0, 1), (3, 1, 0, 0), (1, 1, 2, 0), (1, 0, 3, 0), (3, 0, 0, 1), (1, 3, 0, 0), (2, 0, 1, 1), (3, 0, 1, 0), (1, 2, 0, 1), (2, 2, 0, 0)}
(3) 1-PS = (1, 7/11, -1/11, -17/11) yields a state with 17 characters
Maximal unstable state={(1, 2, 1, 0), (2, 0, 2, 0), (0, 3, 0, 1), (0, 1, 3, 0), (1, 1, 2, 0), (1, 0, 3, 0), (3, 0, 0, 1), (1, 3, 0, 0), (1, 2, 0, 1), (2, 2, 0, 0), (2, 1, 1, 0), (0, 2, 2, 0), (0, 3, 1, 0), (2, 1, 0, 1), (3, 1, 0, 0), (2, 0, 1, 1), (3, 0, 1, 0)}


*************************************************************
SOLUTION TO GIT PROBLEM: STRICTLY POLYSTABLE LOCI
*************************************************************
Group: A3 RepresentationA3(3,1,0,0)
Set of strictly polystable states:
(1) A state with 3 characters
Strictly polystable state={(1, 1, 1, 1), (0, 1, 2, 1), (2, 1, 0, 1)}
(2) A state with 9 characters
Strictly polystable state={(2, 0, 0, 2), (2, 0, 2, 0), (0, 2, 0, 2), (1, 1, 0, 2), (1, 1, 1, 1), (1, 1, 2, 0), (0, 2, 1, 1), (2, 0, 1, 1), (0, 2, 2, 0)}
(3) A state with 5 characters
Strictly polystable state={(2, 0, 0, 2), (0, 2, 2, 0), (1, 0, 3, 0), (0, 3, 0, 1), (1, 1, 1, 1)}
(4) A state with 10 characters
Strictly polystable state={(1, 2, 1, 0), (1, 0, 2, 1), (1, 0, 0, 3), (1, 1, 0, 2), (1, 1, 1, 1), (1, 0, 1, 2), (1, 1, 2, 0), (1, 0, 3, 0), (1, 3, 0, 0), (1, 2, 0, 1)}
(5) A state with 7 characters
Strictly polystable state={(2, 0, 0, 2), (0, 2, 2, 0), (0, 3, 1, 0), (1, 0, 2, 1), (1, 1, 1, 1), (0, 1, 3, 0), (1, 2, 0, 1)}
(6) A state with 3 characters
Strictly polystable state={(2, 0, 0, 2), (0, 2, 2, 0), (1, 1, 1, 1)}
(7) A state with 1 characters
Strictly polystable state={(1, 1, 1, 1)}