LAMBDA-STRUCTURES AND REPRESENTATION RINGS OF COMPACT CONNECTED LIE-GROUPS

We first give an intrinsic characterization of the lambda-rings which are representation rings of compact connected Lie groups. Then we show that the representation ring of a compact connected Lie group G, with its lambda-structure, determines G up to a direct factor which is a p roduct of groups Sp(l) or SO(2l+1). This result is used to show that a compact connected Lie group is determined by its classifying space; d ifferent (and independent) proofs of this result have been given by Za brodsky-Harper, Notbohm and Moller. Our technique also yields a new pr oof of a result of Jackowski, McClure and Oliver on self-homotopy equi valences of classifying spaces. (C) 1997 Elsevier Science B.V.