M. D. Atkinson, G. Pfeiffer and S. J. van Willigenburg,
The -modular descent algebras.
Algebr. Represent. Theory 5 (2002), 101-113.
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
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.
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