The Hilbert series of the polynomial identities for the tensor square of the Grassmann algebra (Q1192100)

Assume \(K\) is a field of characteristic zero, \(E\) the infinite dimensional Grassmann algebra over \(K\), and \(R\) its tensor square (over \(K\)). The authors have calculated the Hilbert series of the relatively free algebras in the variety of algebras \(\text{var }R\) generated by \(R\). The proofs rely on some classical facts concerning sums of Schur functions and on the knowledge of the GL-module structure of the relatively free algebras in the variety \(\text{var }R\).