The degeneration order of simultaneous similarity classes of 3×3 nilpotent matrix tuples is given by rank conditions.
Le Bruyn,Orbits of matrix tuples, Algèbre non commutative, groupes quantiques et in- variants (Reims, 1995), 245-261, Sémin
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Degeneration order of $3\times 3$ nilpotent matrix tuples
The degeneration order of simultaneous similarity classes of 3×3 nilpotent matrix tuples is given by rank conditions.