Left cells and constructible representations
Abstract
Description
We consider the partition of a finite Coxeter group $W$ into left cells with respect to a weight function $L$. In the equal parameter case, Lusztig has shown that the representations carried by the left cells are precisely the so-called constructible ones. We show that this holds for general $L$, if the conjectural properties (P1)--(P15) in Lusztig's book on Hecke algebras with unequal parameters hold for $W,L$. Our proofs use the idea (Gyoja, Rouquier) that left cell representations are projective in the sense of modular representation theory. This also gives partly new proofs for Lusztig's result in the equal parameter case.
31 pages The revised version corrects some minor points and replaces the proof of Cor. 6.3 by a simpler and more elementary argument due to Bernard Leclerc
31 pages The revised version corrects some minor points and replaces the proof of Cor. 6.3 by a simpler and more elementary argument due to Bernard Leclerc