λ-structures and representation rings of compact connected Lie groups Original Research Article

We first give an intrinsic characterization of the λ-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 λ-structure, determines G up to a direct factor which is a product 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; different (and independent) proofs of this result have been given by Zabrodsky-Harper, Notbohm and Møller. Our technique also yields a new proof of a result of Jackowski, McClure and Oliver on self-homotopy equivalences of classifying spaces.