85c:55017 55S10 11T06 15A72

Wilkerson, Clarence ^{(}1-WYNS^{)}

A primer on the Dickson invariants. Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982), 421–434, Contemp. Math., 19, Amer. Math. Soc., Providence, R.I., 1983. As this paper remarks (with references), various topologists have recently made use of the following piece of algebra. Let V be a vector space of dimension n over the finite field F_{q}; let S(V) be the symmetric algebra on V; and let S(V)^{GL(V)} be the subalgebra of elements invariant under GL(V). This subalgebra was determined by L. E. Dickson [Trans. Amer. Math. Soc. 12 (1911), 75–98; Jbuch 42, 136]; it is a polynomial algebra on certain good generators c_{n,i}. The author calls these the “Dickson invariants”. The author’s Section 1 defines the c_{n,i} and proves Dickson’s result. His Section 2 determines the Steenrod operations on the c_{n,i} (assuming that q = p and that one introduces Steenrod operations consistent with the topological applications). His Section 3 deals with various comparable cases, for example, that in which one replaces GL(V) by SL(V). His Section 4 “sketches” the application of the Dickson invariants to recent topological work on the Dyer-Lashof algebra and the lambda-algebra. The author says that his methods are “implicit in” a paper by the reviewer and the author [Ann. of Math. (2) 111 (1980), no. 1, 95–143; MR 81h:55006].

{For the entire collection see MR 84h:55001}.

J. F. Adams (Cambridge)

\begin{matrix}c \\ ◯ \end{matrix} Copyright American Mathematical Society 1985, 1996