Algorithms for orbit closure separation for invariants and semi-invariants of matrices
Harm Derksen, Visu Makam
Algebra and Number Theory | Mathematical Sciences Publishers (MSP) | Published : 2020
We consider two group actions on m-tuples of n ×n matrices with entries in the field K . The first is simultaneous conjugation by GLn and the second is the left-right action of SLn × SLn . Let K be the algebraic closure of the field K . Recently, a polynomial time algorithm was found to decide whether 0 lies in the Zariski closure of the SLn (K )×SLn (K )-orbit of a given m-tuple by Garg, Gurvits, Oliveira and Wigderson for the base field K. An algorithm that also works for finite fields of large enough cardinality was given by Ivanyos, Qiao and Subrahmanyam. A more general problem is the orbit closure separation problem that asks whether the orbit closures of two given m-tuples intersect. F..View full abstract
Awarded by NSF
Derksen was supported by NSF grant DMS-1601229, DMS-2001460 and IIS-1837985. Makam was supported by the University of Melbourne and the NSF grants DMS-1601229, DMS-1638352, CCF-1412958 and CCF-1900460.