The Weiss derivatives of $\BO(-)$ and $\BU(-)$


			Gregory Arone
			University of Chicago
			arone@math.uchicago.edu


We study Michael Weiss' ``orthogonal tower'' of the functors 
$V\mapsto \BO (V)$ and $V\mapsto \BU(V)$. We describe the Weiss 
derivatives of these functors and calculate the homology of
the layers. The orthogonal tower studied here is related to the 
Goodwillie tower of the identity functor in various ways. We find 
that many of the results of Arone-Mahowald and Arone-Dwyer on the 
Goodwillie derivatives of the identity have interesting analogues 
in the context of the Weiss tower, but there are new things to be 
learned from it.