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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

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.