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The \(p\)-modular descent algebras. (English) Zbl 1087.20031
Summary: 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.

20F55 Reflection and Coxeter groups (group-theoretic aspects)
20C20 Modular representations and characters
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
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