Depth and the Steenrod algebra (with an Appendix by J. Lannes)

摘要

Let p be a prime number and Fp[u1,...,un] be the graded polynomial ring on n variables of degree 1 if p=2 and 2 if p>2. Let GLn(Fp) be the group of invertible nxn matrices over Fp. It is known (see [D], [Mu], [LZ3]) that the ring of invariants Dn=(Fp[u1,..., un])GLn(Fp) called the Dickson algebra is a graded polynomial ring Fp[c1,..., cn] on the Dickson invariants.