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Representation Theory

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Relative Kazhdan–Lusztig cells

Author: Meinolf Geck
Journal: Represent. Theory 10 (2006), 481-524
MSC (2000): Primary 20C08; Secondary 20G40
Published electronically: November 14, 2006
MathSciNet review: 2266700
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Abstract: In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group $W$ in a “relative” setting, with respect to a parabolic subgroup $W_I \subseteq W$. This relies on a factorization of the Kazhdan–Lusztig basis $\{\mathbf {C}_w\}$ of the corresponding (multi-parameter) Iwahori–Hecke algebra with respect to $W_I$. We obtain two applications to the “asymptotic case” in type $B_n$, as introduced by Bonnafé and Iancu: we show that $\{\mathbf {C}_w\}$ is a “cellular basis” in the sense of Graham and Lehrer, and we construct an analogue of Lusztig’s canonical isomorphism from the Iwahori–Hecke algebra to the group algebra of the underlying Weyl group of type $B_n$.

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Additional Information

Meinolf Geck
Affiliation: Institut Camille Jordan, bat. Jean Braconnier, Université Lyon 1, 21 av Claude Bernard, F–69622 Villeurbanne Cedex, France
Address at time of publication: Department of Mathematical Sciences, King’s College, Aberdeen University, Aberdeen AB24 3UE, UK
MR Author ID: 272405

Received by editor(s): May 30, 2005
Published electronically: November 14, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.