Generalized Matrix Valued Invariants Original Research Article

The trace ring of generic matrices, Tm, n, can be viewed as the invariant ring of a matrix ring over a polynomial ring or, equivalently, a ring of PGLn(image)-equivariant functions that take values in Mn(image). This paper contains a proof of a structure theorem for the invariants of tensor powers of the above-mentioned matrix ring and shows, in most cases, how this invariant ring relates to (Tcircle times operator r)**. Corollaries to these characterizations include a generalization of the Artin-Schofield Theorem and a description of the projective locus of Tm, n.