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It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In this paper, we make use of the theory of good filtrations along with recent results on the null cone to provide polynomial bounds for matrix semi-invariants in arbitrary characteristic, and consequently for matrix invariants. Our results generalize to invariants and semi-invariants of quivers. [ABSTRACT FROM AUTHOR]

We study the ring R ( n , m ) of invariants for the left–right action of SL n × SL n on m -tuples of n × n complex matrices. We show that R ( 3 , m ) is generated by invariants of degree ≤309 for all m . Then, we use a combinatorial description of the invariants to show that R ( n , m ) cannot be generated by invariants of degree < n 2 for large m . We also compute the Hilbert series for several cases. [ABSTRACT FROM AUTHOR]