Kazhdan–Lusztig Cells and Cellular Bases

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


The aim of this chapter is to develop a general framework for studying the representation theory of Iwahori-Hecke algebras associated to finite Coxeter groups. Using the Kazhdan-Lustig basis, we give a construction of a cellular basis for the Iwahori-Hecke algebra in the sense of Graham and Lehrer. This gives rise to a general theory of “Specht modules” in which Lusztig’s a-function plays, again, a central role. The chapter ends with an elementary treatment of the case where W is the symmetric group.


Weyl Group Parabolic Subgroup Coxeter Group Cell Module Cellular Basis 


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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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