Modules with good filtration and invariant theory
It is a well known theorem of Yu. P. Razmyslov and C. Procesi that all identities with trace of \(n\times n\) matrices over a characteristic zero base field follow from the Cayley-Hamilton identity. This result provides a description of the relations between generators of the ring of invariants of \(m\)-tuples of \(n\times n\) matrices, with respect to the simultaneous conjugation action of the general linear group. A characteristic free generalization was proved by the author [in Algebra Logika 35, No. 4, 433-457 (1996); translation in Algebra Logic 35, No. 4, 241-254 (1996; Zbl 0941.16012)], using results of S. Donkin on modules with good filtration. The present survey outlines this result and the techniques used in its proof. Related works of the author on polynomial invariants of representations of quivers and adjoint action invariants of other classical groups are also discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00049].
scientific article; zbMATH DE number 1683639