Algebras and Representation Theory

, Volume 5, Issue 1, pp 101–113

The p-Modular Descent Algebras

  • M. D. Atkinson
  • G. Pfeiffer
  • S. J. van Willigenburg
Article

DOI: 10.1023/A:1014413413572

Cite this article as:
Atkinson, M.D., Pfeiffer, G. & van Willigenburg, S.J. Algebras and Representation Theory (2002) 5: 101. doi:10.1023/A:1014413413572

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.

descent algebrafinite fieldCoxeter groupCartan matrix

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. D. Atkinson
    • 1
  • G. Pfeiffer
    • 2
  • S. J. van Willigenburg
    • 3
  1. 1.Department of Computer ScienceUniversity of OtagoDunedinNew Zealand
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland
  3. 3.Department of MathematicsCornell UniversityIthacaU.S.A