Relative Kazhdan-Lusztig cells
Author:
Meinolf Geck
Journal:
Represent. Theory 10 (2006), 481-524
MSC (2000):
Primary 20C08; Secondary 20G40
DOI:
https://doi.org/10.1090/S1088-4165-06-00287-1
Published electronically:
November 14, 2006
MathSciNet review:
2266700
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we study the Kazhdan-Lusztig cells of a Coxeter group in a ``relative'' setting, with respect to a parabolic subgroup
. This relies on a factorization of the Kazhdan-Lusztig basis
of the corresponding (multi-parameter) Iwahori-Hecke algebra with respect to
. We obtain two applications to the ``asymptotic case'' in type
, as introduced by Bonnafé and Iancu: we show that
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
.
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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
Email:
geck@maths.abdn.ac.uk
DOI:
https://doi.org/10.1090/S1088-4165-06-00287-1
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.