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Algorithms for orbit closure separation for invariants and semi-invariants of matrices
Algebra & Number Theory  (IF0.938),  Pub Date : 2020-11-19, DOI: 10.2140/ant.2020.14.2791
Harm Derksen, Visu Makam

We consider two group actions on $m$-tuples of $n \times n$ matrices. The first is simultaneous conjugation by $\operatorname{GL}_n$ and the second is the left-right action of $\operatorname{SL}_n \times \operatorname{SL}_n$. We give efficient algorithms to decide if the orbit closures of two points intersect. We also improve the known bounds for the degree of separating invariants in these cases.