Invariants of finite linear groups on relatively free algebras (Q1067010)

Extend the action of a finite group G on a finite dimensional vector space V over an infinite field F to the tensor algebra F(V). The ring R of \(n\times n\) generic matrices over F [on \(d>1\) generators] is defined to be \(F<V>\) factored out by the ideal of identities satisfied by \(n\times n\) matrices over F. If n and the dimension of V are both greater than 1 and F is of characteristic 0, then \(R^ G\) cannot be generated by d elements as an F-algebra. In particular \(R^ G\) is not isomorphic to a ring of generic matrices. Very early in the proof the reduction is made to the case that G is a quasireflection group acting irreducibly on V.