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Lie Groups pp 384-396 | Cite as

Hecke Algebras

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

In this chapter, we will study a certain “Hecke algebra” H k (q) that, as we will see, is a deformation of ℂ[S k ]. The ring H k (q) can actually be defined if q is any complex number, but if q is a prime power, it has a representation-theoretic interpretation. We will see that it is the endomorphism ring of the representation of G = GL(k,F q ), where F q is the finite field with q elements, induced from the trivial representation of the Borel subgroup B of upper triangular matrices in G. The fact that it is a deformation of ℂ[S k ] amounts to a parametrization of a certain set of irreducible representations of G — the so-called unipotent ones — by partitions.

Keywords

Irreducible Representation Irreducible Character Borel Subgroup Double Coset Laurent Polynomial 
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 Science+Business Media New York 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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