The 6×6 equality case of matrix spaces with rank-two commutators · arXivDeskAbstract
Let V⊆M6(C) be a 17-dimensional linear subspace such that rank[S,T]≤2(S,T∈V).
We prove that
, or its transpose, is conjugate to the algebra
⎩⎨⎧A00BλI20CDλI2:A,B,C,D∈M2(C), λ∈C⎭⎬⎫. Consequently, the corresponding closed algebraic locus in
Gr(17,M6(C)) is the disjoint union of two nonsingular irreducible components, each isomorphic to
Fl(2,4;6) . We also prove that the Zariski tangent space at
of the corresponding closed algebraic locus is equal to the tangent space to the conjugacy orbit of
.