## Representation types and 2-primary homotopy groups of
certain compact Lie groups

This 35-page paper was submitted to Homology, Homotopy,
and Applications on April 18, 2003.

** Abstract**
Bousfield has shown how the 2-primary v1-periodic homotopy groups
of certain compact Lie groups can be obtained from their representation
ring with its decomposition into types and its exterior powers
operations. He has formulated a Technical Condition which must
be satisfied in order that he can prove that his description is valid.

We prove that a simply-connected compact simple Lie group
satisfies the Technical Condition if and only if it is **not**
E6 or Spin(4k+2) with k not a 2-power. We then use his description
to give an explicit determination of the 2-primary v1-periodic
homotopy groups of E7 and E8. This completes a program, suggested
to the author by Mimura in 1989, of computing the v1-periodic
homotopy groups of all compact simple Lie groups at all primes.

dvi file and ps file