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hal-00348382, version 1

Hecke group algebras as quotients of affine Hecke algebras at level 0

Florent Hivert () 1, Anne Schilling 2, Nicolas M. Thiéry 2, 3

Journal of Combinatorial Theory, Series A 116, 4 (2009) 844--863

Résumé : The Hecke group algebra $HW_0$ of a finite Coxeter group $W_0$, as introduced by the first and last author, is obtained from $W_0$ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when $W_0$ is the classical Weyl group associated to an affine Weyl group $W$. Namely, we prove that, for $q$ not a root of unity, $HW_0$ is the natural quotient of the affine Hecke algebra through its level 0 representation. We further show that the level 0 representation is a calibrated principal series representation for a suitable choice of character, so that the quotient factors (non trivially) through the principal central specialization. This explains in particular the similarities between the representation theory of the classical 0-Hecke algebra and that of the affine Hecke algebra at this specialization.

  • 1 :  Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes (LITIS)
  • Institut National des Sciences Appliquées (INSA) - Rouen – Université du Havre – Université de Rouen : EA4108
  • 2 :  Department of Mathematics (UC Davis)
  • University of California, Davis
  • 3 :  Laboratoire de Mathématiques d'Orsay (LM-Orsay)
  • CNRS : UMR8628 – Université Paris XI - Paris Sud
  • Domaine : Mathématiques/Théorie des représentations
    Mathématiques/Combinatoire
  • Commentaire : 23 pages – 4 figures
 
  • hal-00348382, version 1
  • http://hal.archives-ouvertes.fr/hal-00348382
  • oai:hal.archives-ouvertes.fr:hal-00348382
  • Contributeur : Nicolas M. Thiéry <>
  • Soumis le : Jeudi 18 Décembre 2008, 16:55:06
  • Dernière modification le : Vendredi 14 Octobre 2011, 09:29:37