The $p$-modular descent algebras
Combinatorics
2007-06-21 v1
Abstract
The concept of descent algebras over a field of characteristic zero is extended to define descent algebras over a field of prime characteristic. Some basic algebraic structure of the latter, including its radical and irreducible modules, is then determined. The decomposition matrix of the descent algebras of Coxeter group types , , and are calculated, and used to derive a description of the decomposition matrix of an arbitrary descent algebra. The Cartan matrix of a variety of descent algebras over a finite field is then obtained.
Cite
@article{arxiv.0706.2908,
title = {The $p$-modular descent algebras},
author = {M. D. Atkinson and G. Pfeiffer and S. J. van Willigenburg},
journal= {arXiv preprint arXiv:0706.2908},
year = {2007}
}