Subject: Question for the list From: Johannes Huebschmann Date: Wed, 7 Dec 2005 14:07:09 +0100 (CET) Here is a question related to the discussion on invariants a while ago: Consider the algebra of polynomials in two sets $z_1,...,z_n$ and $w_1,...,w_n$ of variables, endowed with the obvious action of the symmetric group $S_n$ which permutes the variables separately. According to a classical result which goes back to the 19th century (at least), the algebra of $S_n$-invariants is generated by the elementary bisymmetric functions. These are obtained from the elementary symmetric functions by polarization. Is there a place in the literature where a finite system of defining relations has been worked out, for $n=3$ or perhaps for higher $n$? Classical results yield systems with infinitely many generators and infinitely many defining relations, see e.g. F. Vaccarino, The ring of multisymmetric functions, Ann. Inst. Four. 55 (2005) 717-731. Johannes Huebschmann