For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of ""O -noninversions"" of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.
Victor Reiner, University of Minnesota, Minneapolis, Minnesota.Franco Saliola, Universite du Quebec a Montreal, Canada.Volkmar Welker, Philipps-Universitaet Marburg, Germany.
IntroductionDefining the operatorsThe case where O contains only hyperplanesEquivariant theory of BHR random walksThe family ? (2 k ,1 n?2k)The original family ? (k,1 n?k)AcknowledgementsAppendix A. G n -module decomposition of ? (k,1 n?k)BibliographyList of SymbolsIndex