P.S. A related remark: we all know that polynomial finite-dim irreps of GL(V) are contained in V^{\otimes p}\otimes (V^*)^{\otimes q}, and this is also suggested by the Stone-Weierstrass viewpoint, at least in the complex case, as we need polynomials in z and z-bar, which precisely means polynomials in matrix elements of V and V^*.

One of standard versions of Stone-Weierstrass is "Suppose X is a compact Hausdorff space and A is a subalgebra of C(X) which contains a non-zero constant function. Then A is dense in C(X) if and only if it separates points." I think you can find it in Rudin's analysis textbook in this form. However, in the case of finite groups, you don't need that much (since matrix elements of U separate points of G/H, we embed G/H in the (dim(U))^2-dimensional coordinate vector space and do polynomial interpolation), but for the case of SU(n) or something, Stone-Weierstrass is handy.

A very obvious addition to what you said about B_n - in general, if you have a combinatorial description of conjugacy class in G, classes of the semidirect product of S_n and G^n have a closely related description as well, and that shows up in various situations.

okay, I don't know what happened to the long google books url in the previous comment, so let me re-type it in a better way: tinyurl.com/prasolov

@jp: sorry for not providing a reference - I was in a hurry. An excellent source on many a theorem about polynomials is <a href="books.google.com/… book</a> (for facts I am referring to, see page 53, Dumas' theorem (and a bit before this theorem), but there are lots of other useful things there).

@Gjergji: good point - I was thinking along the same line after I walked in the street having written that suggestion. However, what you say about how to mend my example seems to be a good idea.

Just for the record: for an augmented algebra, the bar homology of A' is nothing but Tor_A(k,k) (see the normalized bar resolution of k) - so it's something not that much neglected as you are saying!

A brief remark on the last paragraph of your answer - it seems that some info on resolutions of Specht modules over Z (actually, maybe all possible information) can be extracted from arxiv.org/abs/0803.4382

From what I recall from your paper, in (a) there should be 3 coordinates, not 4 (the pencil is pulled back from P^2), am I right? Just want to clarify the story (it was some time ago when I read the paper).

There was some other obvious reference I am missing - I'll let you know if it comes to my mind.