Linckelmann, M. & Schroll, S. (2005). A twosided qanalogue of the Coxeter complex. Journal of Algebra, 289(1), pp. 128134. doi: 10.1016/j.jalgebra.2005.03.026,

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Abstract
M. Cabanes and J. Rickard showed in [3] that the AlvisCurtis character duality of a finite group of Lie type is induced in non defining characteristic ℓ by a derived equivalence given by tensoring with a bounded complex X, and they further conjecture that this derived equivalence should actually be a homotopy equivalence. Following a suggestion of R. Kessar, we show here for the special case of principal blocks of general linear groups with abelian Sylowℓsubgroups that this is true, by an explicit verification relating the complex X to the Coxeter complex of the corresponding Weyl group.
Item Type:  Article 

Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/1897 
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