Relative Kazhdan--Lusztig cells

Details Relative Kazhdan--Lusztig cells Relative Kazhdan--Lusztig cells

2005-04-11

arxiv.org/abs/math/0504216v2

Mathematics

Representation Theory

50 pages, submitted; the revised version corrects some misprints

Scientific paper

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 $\{C_w\}$ 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 Bonnaf\'e--Iancu: we show that $\{C_w\}$ is a ``cellular basis'' in the sense of Graham--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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