0 This Sk(V) × S~(V). 11. splitting map strong ~U(V)+ to Sk(V) + is F ( V ) - h o m o t o p i c the space S0(V) = P(V), with the following f o r m of the Sk(V) + " inclusion r e t r a c t i o n , in the denotes SI(V) be c o n c e r n e d equivariant recent and Richter. k ~ 0, the k = 0, w i t h see a l s o THEOREM will F k and a n e ~ u i v a r i a n t restriction (Here section is a s t r e n g t h e n e d F(V)-equivariant F(V)-module [6]; for a u n i q u e geometry.

11] D. (HP ~) generators", J . P u r e and App. A l g . , 14 (1979) 3 1 5 - 2 2 . Historical Adams, "On t h e g r o u p s " F o r m a l 6 r o u p s and a p p l i c a t i o n s " , "p-adic L-functions Riordan, J ( X ) - IV", T o p o l o g y 5 (1966) "Combinatorial f o r CM f i e l d s " , Identities", 21-71. decomposable Academic P r e s s Invent. Lecture BU and t h e (1978). Math. 49 ( 1 9 7 8 ) . the iterated Academic P r e s s . and t h e p r i m i t i v e Note T h i s p a p e r i s a r e v i s e d v e r s i o n o f a p r e p r i n t f i r s t p r e p a r e d i n e a r l y 1984 but never published.

The original The result case of J a m e s [2]. ) 5 inclusion P(V)+ c There is a F ( V ) - e q u i v a r i a n t ~ QU(V)+ given by a m a p stable ~u(v)+ M a p ( E n d ( V ) + , End(V) + A P(V)+). 11), by l o o k i n g we as in the d e d u c t i o n H = F(V). 11). of ~U(V) and a of a is the : S1 ~ i~ 47 is a map w i t h a(1) Sk(V)F(V) = 0, a(z) = a(z). 12) is empty if n % k, equal to {p~} i_ff k = rn, and the i n c l u s i o n Sk(V) F(V) r for k > 0. Thus: > (~kU(V)) F(V) is a h o m o t o p y e q u i v a l e n c e This is at least c o n s i s t e n t w i t h the truth of the conjec- ture.