Hilbert series and degree bounds for matrix (semi-)invariants

الأصل · EN

We study the ring R(n,m) of invariants for the left-right action of SLₙ × SLₙ on m-tuples of n by n complex matrices. We show that R(3,m) is generated by invariants of degree less equal 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 < n² for large m. We also compute the Hilbert series for several cases.