We describe a minimal unstable module presentation over the Steenrod algebra for the odd-primary cohomology of infinite-dimensional complex projective space and apply it to obtain a minimal algebra presentation for the cohomology of the classifying space of the infinite unitary group. We also show that there is a unique Steenrod module structure on any unstable cyclic module that has dimension one in each complex degree (half the topological degree) with a fixed alpha-number (sum of `digits') and is zero in other degrees.
Homology, Homotopy and Applications, Vol. 9 (2007), No. 2, pp.363-395.
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