Minimal generating or separating sets for 4×4 matrix invariants

Determine whether the minimal bihomogeneous generating set found by Drensky and Sadikova for C[Mat_4^2]^G is minimal as an algebra generating set or as a separating set.

Background

For two 4×4 matrices under simultaneous conjugation, Drensky and Sadikova constructed a minimal set of bihomogeneous polynomials generating the invariant algebra. The paper distinguishes this construction from the unresolved question of whether the set is minimal in the relevant generating or separating senses.

Resolving the question would clarify the relationship between explicit invariant generators and cardinality-minimal separating sets in this case.