The $p$-modular descent algebras

Details The $p$-modular descent algebras The $p$-modular descent algebras

2007-06-20

arxiv.org/abs/0706.2908v1

Algebr. Represent. Theory 5:101-113 (2002)

Mathematics

Combinatorics

21 pages; Original version of Algebr. Represent. Theory 5:101-113 (2002). Journal version can be found at http://www.math.ub

Scientific paper

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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