Hecke algebras arise naturally in the representation theory of reductive groups over finite or <i>p</i>-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under “long enough” translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type <i>Ğ</i><sub>2</sub> into cells for a whole class of weight functions.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:446609 |
| Date | January 2008 |
| Creators | Guilhot, Jérémie |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ueaeprints.uea.ac.uk/20105/ |
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