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The p-Modular Descent Algebras M.D. Atkinson

Summary: The p-Modular Descent Algebras
M.D. Atkinson
S.J. van Willigenburg 1
School of Mathematical and Computational Sciences
North Haugh, St Andrews, Fife KY16 9SS, UK
G. Pfei er
Department of Mathematics
National University of Ireland, Galway, Ireland
Solomon's descent algebras are studied over elds of prime characteris-
tic. Their radical and irreducible modules are determined. It is shown how
their representation theory can be related to the representation theory in
elds of characteristic zero.
1 Introduction
Descent algebras are non-commutative, non-semi-simple algebras associated with
nite Coxeter groups. They were rst discovered by Solomon in the 1970's and
for the last 10 years have been studied intensively [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14,
17]. Previous work has concentrated on the case that the underlying eld has
characteristic zero. In this paper we study descent algebras over elds of prime
characteristic. We determine the radical of a descent algebra in characteristic


Source: Atkinson, Mike - Department of Computer Science, University of Otago


Collections: Computer Technologies and Information Sciences