Induced vector bundles of corepresentations and Real representations
In his work on maps between classifying spaces of compact Lie groups, Frank Adams studied the image of the natural homomorphism α: R(G)—>K(BG) for a compact Lie group G. Specififically he proved that the image of α coincides with the subgroup of elements of K(BG) generated by those elements with only fifinitely many non-zero exterior powers when π0(G) is a p-group for any prime p. Bob Oliver proved the real analogue of this result. Atiyah and Segal introduced the notion of Real groups, Real representations and Real vector bundles in late 60s. A few years later, Karoubi studied a wider class of groups which he still called Real groups. They were unaware that Real representations were studied by Eugene Wigner at least 10 years before Atiyah and Segal in the name of corepresentations. We will give a summary of the theory developed by Wigner and then go on to prove that the Real case of the above mentioned result of Frank Adams holds when π0 of the underlying group is a 2-group, but fails to hold when π0 is a p-group for p≠2.
Lam Siu-Por obtained his PhD in algebraic topology in 1983, under the supervision of Professor Frank Adams. He used to be the Associate Professor at the Chinese University of Hong Kong and retired to England. He has taught several courses at the Capital Normal University in Beijing.