Subject: Re: two postings From: Clarence W Wilkerson Jr Date: Wed, 07 Dec 2005 14:39:50 -0500 The paper of Priddy-Milgram might have some relevant material: *MR0885113* *(88j:20038)* Milgram, R. James (1-STF) ; Priddy, Stewart B. (1-NW) * Invariant theory and $H\sp *({\rm GL}\sb n(*F*\sb p); *F*\sb p)$. * Proceedings of the Northwestern conference on cohomology of groups (Evanston, Ill., 1985). /J. Pure Appl. Algebra/ * 44 * (1987), no. 1-3, 291--302. 20G10 (18F25 19D55) Don Davis wrote: > Two postings: A new question and a response to an old one > .....................DMD > _____________________________________________________________ > > 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 > ________________________________________________________ >