Algebras and Representation Theory

, Volume 5, Issue 1, pp 101-113

First online:

The p-Modular Descent Algebras

  • M. D. AtkinsonAffiliated withDepartment of Computer Science, University of Otago
  • , G. PfeifferAffiliated withDepartment of Mathematics, National University of Ireland
  • , S. J. van WilligenburgAffiliated withDepartment of Mathematics, Cornell University

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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.

descent algebra finite field Coxeter group Cartan matrix