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Mathematische Zeitschrift

, Volume 271, Issue 1–2, pp 373–397 | Cite as

Affine cellularity of affine Hecke algebras of rank two

  • Jérémie Guilhot
  • Vanessa Miemietz
Article

Abstract

We show that affine Hecke algebras of rank two with generic parameters are affine cellular in the sense of Koenig–Xi.

Keywords

Weyl Group Left Ideal Matrix Ring Principal Ideal Domain Left Cell 
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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References

  1. 1.
    Bonnafé C.: Semicontinuity properties of Kazhdan-Lusztig cells. N.Z. J. Math. 39, 171–192 (2009)MATHGoogle Scholar
  2. 2.
    Bourbaki, N.: Groupes et algèbres de Lie, Chaps. 4–6. Hermann, Paris (1968); Masson, Paris (1981)Google Scholar
  3. 3.
    Geck M.: On the induction of Kazhdan-Lusztig cells. Bull. Lond. Math. Soc. 35, 608–614 (2003)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Geck M.: Hecke algebras of finite type are cellular. Invent. Math. 169, 501–517 (2007)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Graham J.J., Lehrer G.I.: Cellular algebras. Invent. Math. 123, 1–34 (1996)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Guilhot, J.: Some computations about Kazhdan-Lusztig cells in affine Weyl groups of rank 2. http://arxiv.org/abs/0810.5165
  7. 7.
    Guilhot J.: Generalized induction of Kazhdan-Lusztig cells. Ann. Inst. Fourier 59, 1385–1412 (2009)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Guilhot J.: Kazhdan-Lusztig cells in affine Weyl groups of rank 2. Int. Math. Res. Not. 2010, 3422–3462 (2010)MathSciNetMATHGoogle Scholar
  9. 9.
    Koenig, S., Xi, C.: Affine cellular algebras. Preprint. http://math.bnu.edu.cn/ccxi/Papers/Articles/affcell.pdf
  10. 10.
    Lusztig G.: Hecke algebras and Jantzen’s generic decomposition patterns. Adv. Math. 37, 121–164 (1980)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Lusztig, G.: Hecke algebras with unequal parameters. In: CRM Monograph Series, vol. 18. Amer. Math. Soc., Providence (2003)Google Scholar
  12. 12.
    Opdam E., Solleveld M.: Homological algebra for affine Hecke algebras. Adv. Math. 220(5), 1549–1601 (2009)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of MathematicsUniversity of East AngliaNorwichUK

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