Abstract
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.
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© 2011 Springer-Verlag London Limited
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Geck, M., Jacon, N. (2011). Kazhdan–Lusztig Cells and Cellular Bases. In: Representations of Hecke Algebras at Roots of Unity. Algebra and Applications, vol 15. Springer, London. https://doi.org/10.1007/978-0-85729-716-7_2
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DOI: https://doi.org/10.1007/978-0-85729-716-7_2
Publisher Name: Springer, London
Print ISBN: 978-0-85729-715-0
Online ISBN: 978-0-85729-716-7
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