Author: Peter Webb
email: webb@math.umn.edu
Address:
School of Mathematics,
University of Minnesota,
Minneapolis MN 55455

Title:
Standard stratifications of EI categories and Alperin's weight conjecture

Abstract:
We characterize the finite EI categories whose representations are standardly 
stratified with respect to the natural preorder on the simple representations. 
The orbit category of a finite group with respect to any set of subgroups is 
always such a category. Taking the subgroups to be the $p$-subgroups of the 
group, we reformulate Alperin's weight conjecture in terms of the standard 
and proper costandard representations of the orbit category. We do this using 
the properties of the Ringel dual construction and a theorem of Dlab, which 
have elsewhere been described for standardly stratified algebras where there 
is a partial order on the simple modules. We indicate that these results hold 
in the generality of an algebra whose simple modules are preordered, rather 
than partially ordered.

Preprint: June 2005.
Revised: February 2006.
To appear: Journal of Algebra.