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Hecke Algebras and Finite Groups of Lie Type

Part of the Algebra and Applications book series (AA, volume 15)

Abstract

Here we explain the fundamental connections between the theory of Iwahori-Hecke algebras and representations of a finite group of Lie type G. We study the modular representation theory of G and show how our previous results on “cell data” and “canonical basic sets” leads to a natural parametrization of the modular irreducible representations of G which admit non-zero vectors fixed by a Borel subgroup. This generalises classical results due to Bourbaki, Iwahori, Tits, which are concerned with the characteristic 0 situation. We then discuss a number of examples and open problems. This includes a conjectural classification of all the irreducible representations of G in the “non-defining characteristic case”.

Keywords

Irreducible Representation Finite Group Composition Factor Discrete Valuation Ring Cuspidal Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of AberdeenAberdeenUK
  2. 2.UFR Sciences et TechniquesUniversité de Franche-ComtéBesanconFrance

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