Abstract
In this first chapter, we introduce the main objects of our study: Finite Coxeter groups, generic Iwahori-Hecke algebras, and their representations. An Iwahori-Hecke algebra H is here seen as a deformation of the group algebra of a finite Coxeter group W, where the deformation depends on a choice of a certain “weight function” L. Following Lusztig, to each simple module E of a Coxeter group over ℂ, we canonically associate a numerical invariant a E . The study of the a-function, and its subtle relation with Kazhdan–Lusztig basis of H, will be one of the main themes of this book. As a first step we shall introduce an “asymptotic” version of H and use this to define partitions of W into left, right and two sided cells.
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© 2011 Springer-Verlag London Limited
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Geck, M., Jacon, N. (2011). Generic Iwahori–Hecke Algebras. 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_1
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DOI: https://doi.org/10.1007/978-0-85729-716-7_1
Publisher Name: Springer, London
Print ISBN: 978-0-85729-715-0
Online ISBN: 978-0-85729-716-7
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