M. D. Atkinson, G. Pfeiffer and S. J. van Willigenburg,
# The $p$-modular descent algebras.

*Algebr. Represent. Theory* **5** (2002), 101-113.

## 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.
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