Relative Kazhdan–Lusztig cells

Geck, Meinolf

doi:10.1090/S1088-4165-06-00287-1

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
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Abstract: In this paper, we study the Kazhdan-Lusztig cells of a Coxeter group 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 . We obtain two applications to the ``asymptotic case'' in type , 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 .

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