The $p$modular descent algebras
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 $A$, $B$, and $D$ 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2007
 arXiv:
 arXiv:0706.2908
 Bibcode:
 2007arXiv0706.2908A
 Keywords:

 Mathematics  Combinatorics;
 20F32
 EPrint:
 21 pages